Exhibit 3.1

AMENDMENT NO. 1 TO

SECOND AMENDED AND RESTATED BY-LAWS

OF

ANSYS, INC.

Article I, Section 2 and Article II, Section 3 of the Second Amended and Restated By-laws of ANSYS, INC. are hereby deleted in their entirety and replaced with the following:

Article I, Section 2:

“SECTION 2. Matters to be Considered at Annual Meetings. At any annual meeting of stockholders or any special meeting in lieu of annual meeting of stockholders (the “Annual Meeting”), only such business shall be conducted, and only such proposals shall be acted upon, as shall have been properly brought before such Annual Meeting. To be considered as properly brought before an Annual Meeting, business must be: (a) brought before the meeting by, or at the direction of, the Board of Directors, or (b) otherwise properly brought before the meeting by any holder of record (both as of the time notice of such proposal is given by the stockholder as set forth below and as of the record date for the Annual Meeting in question) of any shares of capital stock of the Corporation entitled to vote at such Annual Meeting who complies with the requirements set forth in this Section 2 and, with respect to nominations, Article II Section 3 of these By-laws. For the avoidance of doubt, for a stockholder to bring business or nominations before an Annual Meeting (other than matters properly brought under Rule 14a-8 (or any successor rule) under the Securities Exchange Act of 1934, as amended (the “Exchange Act”)), such stockholder must comply with the procedures set forth in this Article I, Section 2 of this By-law with respect to business other than nominations and with the procedures set forth in Article II, Section 3 with respect to nominations, and these procedures shall be the exclusive means for a stockholder to bring such business or nominations properly before an Annual Meeting. In addition to the other requirements set forth in this By-law, for any proposal of business to be considered at an Annual Meeting, it must be a proper subject for action by stockholders of the Corporation under Delaware law.

In addition to any other applicable requirements, for business (other than nominations, which are governed by Article II, Section 3) to be properly brought before an Annual Meeting by a stockholder of record of any shares of capital stock entitled to vote at such Annual Meeting, such stockholder shall: (i) give Timely Notice (as defined below) in writing as required by this Section 2 to the Secretary of the Corporation, (ii) provide any updates or supplements to such notice at the times and in the forms required by this Section 2 and (iii) be present at such meeting, either in person or by a representative. For the first Annual Meeting following the initial public offering of common stock of the Corporation, a stockholder’s notice shall be timely if delivered to, or mailed to and received by, the Corporation at its principal executive office not later than the close of business on the later of (A) the 75th day prior to the scheduled date of such Annual Meeting or (B) the 15th day following the day on which public announcement of the date of such Annual Meeting is first made by the Corporation. For all subsequent Annual Meetings, a stockholder’s notice shall be timely if delivered to, or mailed to and received by, the Corporation at its principal executive office not less than 75 days nor more than 120 days prior to the anniversary date of the immediately preceding Annual Meeting (the “Anniversary Date”); provided, however, that in the event the Annual Meeting is scheduled to be held on a date more

than 30 days before the Anniversary Date or more than 60 days after the Anniversary Date, a stockholder’s notice shall be timely if delivered to, or mailed to and received by, the Corporation at its principal executive office not later than the close of business on the later of (A) the 75th day prior to the scheduled date of such Annual Meeting or (B) the 15th day following the day on which public announcement of the date of such Annual Meeting is first made by the Corporation (such notice delivered within the time periods set forth in this sentence or the immediately preceding sentence shall be referred to as “Timely Notice”).

For purposes of these By-laws, “public announcement” shall mean: (i) disclosure in a press release reported by the Dow Jones News Service, Associated Press or comparable national news service, (ii) a report or other document filed publicly with the Securities and Exchange Commission (including, without limitation, a Form 8-K), or (iii) a letter or report sent to stockholders of record of the Corporation at the time of the mailing of such letter or report.

A stockholder’s Timely Notice to the Secretary shall set forth as to each matter proposed to be brought before an Annual Meeting: (a) a brief description of the business the stockholder desires to bring before such Annual Meeting and the reasons for conducting such business at such Annual Meeting; (b) as to the stockholder giving the notice and the beneficial owner(s), if any, on whose behalf the proposal is made: (i) the name and address of such stockholder, as they appear on the Corporation’s books, and of such beneficial owner(s); (ii) (A) the class or series and number of shares of the Corporation which are, directly or indirectly, owned beneficially and of record by such stockholder and any such beneficial owner(s), (B) any derivative, swap or other transaction or series of transactions engaged in, directly or indirectly, by such stockholder and/or any such beneficial owner(s) the purpose or effect of which is to give such stockholder and/or any such beneficial owner(s) economic benefit and/or risk similar to ownership of shares of any class or series of the Corporation, in whole or in part, including due to the fact that such derivative, swap or other transaction provides, directly or indirectly, the opportunity to profit or avoid a loss from any increase or decrease in the value of shares of any class or series of the Corporation (“Synthetic Equity Interests”) and such disclosure shall identify the counterparty to each such Synthetic Equity Interest and shall include, for each such Synthetic Equity Interest, whether or not (x) such Synthetic Equity Interest conveys any voting rights, directly or indirectly, in such shares to such stockholder and/or any such beneficial owner(s), (y) such Synthetic Equity Interest is required to be, or is capable of being, settled through delivery of such shares and (z) such stockholder, any such beneficial owner(s) and/or, to their knowledge, the counterparty to such Synthetic Equity Interest has entered into other transactions that hedge or mitigate the economic effect of such Synthetic Equity Interest, (C) any proxy (other than a revocable proxy given in response to a public proxy solicitation made pursuant to, and in accordance with, the Exchange Act), agreement, arrangement, understanding or relationship pursuant to which such stockholder and/or any such beneficial owner(s) has or shares a right to vote any shares of any class or series of the Corporation, (D) any agreement, arrangement, understanding or relationship (which disclosure shall identify the counterparty thereto), including any hedge, repurchase or similar so-called “stock borrowing” agreement or arrangement, engaged in, directly or indirectly, by such stockholder and/or any such beneficial owner(s), the purpose or effect of which is to mitigate loss to, reduce the economic risk of shares of any class or series of the Corporation by, manage the risk of share price changes for, or increase or decrease the voting power of, such stockholder and/or any such beneficial owner(s) with respect to the shares of any class or series of the Corporation, or which provides, directly or indirectly,

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the opportunity to profit from any decrease in the value of the shares of any class or series of the Corporation (“Short Interests”), (E) any rights to dividends or other distributions on the shares of any class or series of the Corporation owned beneficially by such stockholder and/or any such beneficial owner(s) that are separated or separable from the underlying shares of the Corporation, (F) any performance-related fees (other than an asset based fee) that such stockholder and/or any such beneficial owner(s) is entitled to based on any increase or decrease in the value of shares of any class or series of the Corporation, any Synthetic Equity Interests or Short Interests, if any (the disclosures to be made pursuant to the foregoing clauses (A) through (F) are referred to as “Material Ownership Interests”); (c) the names and addresses of other stockholders known by the stockholder and/or any such beneficial owner(s) proposing such business to support such proposal, and the class and number of shares of the Corporation’s capital stock beneficially owned by such other stockholders; and (d) any material interest of the stockholder and/or any such beneficial owner(s) proposing to bring such business before such meeting (or any other stockholders known to be supporting such proposal) in such proposal.

A stockholder providing Timely Notice of business proposed to be brought before an Annual Meeting shall further update and supplement such notice, if necessary, so that the information (including, without limitation, the Material Ownership Interests information) provided or required to be provided in such notice pursuant to this By-law shall be true and correct as of the record date for the meeting and as of the date that is ten (10) business days prior to such Annual Meeting, and such update and supplement shall be delivered in writing to the Secretary at the principal executive offices of the Corporation not later than the close of business on the fifth (5th) business day after the record date for the meeting (in the case of the update and supplement required to be made as of the record date), and not later than the close of business on the eighth (8th) business day prior to the date for the meeting (in the case of the update and supplement required to be made as of ten (10) business days prior to the meeting).

If the Board of Directors or a designated committee thereof determines that any stockholder proposal was not made in a timely fashion in accordance with the provisions of this Section 2 or that the information provided in a stockholder’s notice does not satisfy the information requirements of this Section 2 in any material respect, such proposal shall not be presented for action at the Annual Meeting in question. If neither the Board of Directors nor such committee makes a determination as to the validity of any stockholder proposal in the manner set forth above, the presiding officer of the Annual Meeting shall determine whether the stockholder proposal was made in accordance with the terms of this Section 2. If the presiding officer determines that any stockholder proposal was not made in a timely fashion in accordance with the provisions of this Section 2 or that the information provided in a stockholder’s notice does not satisfy the information requirements of this Section 2 in any material respect, such proposal shall not be presented for action at the Annual Meeting in question. If the Board of Directors, a designated committee thereof or the presiding officer determines that a stockholder proposal was made in accordance with the requirements of this Section 2, the presiding officer shall so declare at the Annual Meeting and ballots shall be provided for use at the meeting with respect to such proposal.

Notwithstanding the foregoing provisions of this By-Law, a stockholder shall also comply with all applicable requirements of the Exchange Act, and the rules and regulations thereunder with respect to the matters set forth in this By-Law. Nothing in this By-Law shall be deemed to affect

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any rights of stockholders to have proposals included in the Corporation’s proxy statement pursuant to Rule 14a-8 (or any successor rule) under the Exchange Act and, to the extent required by such rule, have such proposals considered and voted on at an Annual Meeting.”

Article II, Section 3:

“SECTION 3. Director Nominations. Nominations of candidates for election as directors of the Corporation at any Annual Meeting may be made only (a) by, or at the direction of, a majority of the Board of Directors or (b) by any holder of record (both as of the time notice of such nomination is given by the stockholder as set forth below and as of the record date for the Annual Meeting in question) of any shares of the capital stock of the Corporation entitled to vote at such Annual Meeting who complies with the timing, informational and other requirements set forth in this Section 3. Any stockholder who has complied with the timing, informational and other requirements set forth in this Section 3 and who seeks to make such a nomination, or his, her or its representative, must be present in person at the Annual Meeting. Only persons nominated in accordance with the procedures set forth in this Section 3 shall be eligible for election as directors at an Annual Meeting.

Nominations, other than those made by, or at the direction of, the Board of Directors, shall be made pursuant to timely notice in writing to the Secretary of the Corporation as set forth in this Section 3. For the first Annual Meeting following the initial public offering of common stock of the Corporation, a stockholder’s notice shall be timely if delivered to, or mailed to and received by, the Corporation at its principal executive office not later than the close of business on the later of (A) the 75th day prior to the scheduled date of such Annual Meeting or (B) the 15th day following the day on which public announcement of the date of such Annual Meeting is first made by the Corporation. For all subsequent Annual Meetings, a stockholder’s notice shall be timely if delivered to, or mailed to and received by, the Corporation at its principal executive office not less than 75 days nor more than 120 days prior to the Anniversary Date; provided, however, that in the event the Annual Meeting is scheduled to be held on a date more than 30 days before the Anniversary Date or more than 60 days after the Anniversary Date, a stockholder’s notice shall be timely if delivered to, or mailed and received by, the Corporation at its principal executive office not later than the close of business on the later of (i) the 75th day prior to the scheduled date of such Annual Meeting or (ii) the 15th day following the day on which public announcement of the date of such Annual Meeting is first made by the Corporation.

A stockholder’s notice to the Secretary shall set forth as to each person whom the stockholder proposes to nominate for election or re-election as a director: (i) the name, age, business address and residence address of such person, (ii) the principal occupation or employment of such person, (iii) the class and number of shares of the Corporation’s capital stock which are beneficially owned by such person on the date of such stockholder notice, and (iv) the consent of each nominee to serve as a director if elected. Such stockholder’s notice to the Secretary shall further set forth as to the stockholder giving such notice: (a) as to the stockholder giving the notice and the beneficial owner(s), if any, on whose behalf the proposal is made: (i) the name and address of such stockholder, as they appear on the Corporation’s books, and of such beneficial owner(s); (ii) (A) the class or series and number of shares of the Corporation which are, directly or indirectly, owned beneficially and of record by such stockholder and any such

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beneficial owner(s), (B) any derivative, swap or other transaction or series of transactions engaged in, directly or indirectly, by such stockholder and/or any such beneficial owner(s) the purpose or effect of which is to give such stockholder and/or any such beneficial owner(s) economic benefit and/or risk similar to ownership of shares of any class or series of the Corporation, in whole or in part, including due to the fact that such derivative, swap or other transaction provides, directly or indirectly, the opportunity to profit or avoid a loss from any increase or decrease in the value of shares of any class or series of the Corporation (“Synthetic Equity Interests”) and such disclosure shall identify the counterparty to each such Synthetic Equity Interest and shall include, for each such Synthetic Equity Interest, whether or not (x) such Synthetic Equity Interest conveys any voting rights, directly or indirectly, in such shares to such stockholder and/or any such beneficial owner(s), (y) such Synthetic Equity Interest is required to be, or is capable of being, settled through delivery of such shares and (z) such stockholder, any such beneficial owner(s) and/or, to their knowledge, the counterparty to such Synthetic Equity Interest has entered into other transactions that hedge or mitigate the economic effect of such Synthetic Equity Interest, (C) any proxy (other than a revocable proxy given in response to a public proxy solicitation made pursuant to, and in accordance with, the Exchange Act), agreement, arrangement, understanding or relationship pursuant to which such stockholder and/or any such beneficial owner(s) has or shares a right to vote any shares of any class or series of the Corporation, (D) any agreement, arrangement, understanding or relationship (which disclosure shall identify the counterparty thereto), including any hedge, repurchase or similar so-called “stock borrowing” agreement or arrangement, engaged in, directly or indirectly, by such stockholder and/or any such beneficial owner(s), the purpose or effect of which is to mitigate loss to, reduce the economic risk of shares of any class or series of the Corporation by, manage the risk of share price changes for, or increase or decrease the voting power of, such stockholder and/or any such beneficial owner(s) with respect to the shares of any class or series of the Corporation, or which provides, directly or indirectly, the opportunity to profit from any decrease in the value of the shares of any class or series of the Corporation (“Short Interests”), (E) any rights to dividends or other distributions on the shares of any class or series of the Corporation owned beneficially by such stockholder and/or any such beneficial owner(s) that are separated or separable from the underlying shares of the Corporation, (F) any performance-related fees (other than an asset based fee) that such stockholder and/or any such beneficial owner(s) is entitled to based on any increase or decrease in the value of shares of any class or series of the Corporation, any Synthetic Equity Interests or Short Interests, if any (the disclosures to be made pursuant to the foregoing clauses (A) through (F) are referred to as “Material Ownership Interests”); (b) the names and addresses of other stockholders known by the stockholder and/or any such beneficial owner(s) proposing such nomination(s) to support such nominee(s), and the class and number of shares of the Corporation’s capital stock beneficially owned by such other stockholders; and (c) a description of all arrangements or understandings among such stockholder and/or any such beneficial owner(s) and each proposed nominee and any other person or persons (naming such person or persons) pursuant to which the nomination or nominations are to be made by such stockholder.

A stockholder providing timely notice under this Section 3 of proposed nominations to be brought before an Annual Meeting shall further update and supplement such notice, if necessary, so that the information (including, without limitation, the Material Ownership Interests information) provided or required to be provided in such notice pursuant to this Section 3 shall be true and correct as of the record date for the meeting and as of the date that is ten (10)

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business days prior to such Annual Meeting, and such update and supplement shall be delivered in writing to the Secretary at the principal executive offices of the Corporation not later than the close of business on the fifth (5th) business day after the record date for the meeting (in the case of the update and supplement required to be made as of the record date), and not later than the close of business on the eighth (8th) business day prior to the date for the meeting (in the case of the update and supplement required to be made as of ten (10) business days prior to the meeting).

If the Board of Directors or a designated committee thereof determines that any stockholder nomination was not made in accordance with the terms of this Section 3 or that the information provided in a stockholder’s notice does not satisfy the informational requirements of this Section 3 in any material respect, then such nomination shall not be considered at the Annual Meeting in question. If neither the Board of Directors nor such committee makes a determination as to whether a nomination was made in accordance with the provisions of this Section 3, the presiding officer of the Annual Meeting shall determine whether a nomination was made in accordance with such provisions. If the presiding officer determines that any stockholder nomination was not made in accordance with the terms of this Section 3 or that the information provided in a stockholder’s notice does not satisfy the informational requirements of this Section 3 in any material respect, then such nomination shall not be considered at the Annual Meeting in question. If the Board of Directors, a designated committee thereof or the presiding officer determines that a nomination was made in accordance with the terms of this Section 3, the presiding officer shall so declare at the Annual Meeting and ballots shall be provided for use at the meeting with respect to such nominee.

Notwithstanding anything to the contrary in the second sentence of the second paragraph of this Section 3, in the event that the number of directors to be elected to the Board of Directors of the Corporation is increased and there is no public announcement by the Corporation naming all of the nominees for director or specifying the size of the increased Board of Directors at least 75 days prior to the Anniversary Date, a stockholder’s notice required by this Section 3 shall also be considered timely, but only with respect to nominees for any new positions created by such increase, if such notice shall be delivered to, or mailed to and received by, the Corporation at its principal executive office not later than the close of business on the 15th day following the day on which such public announcement is first made by the Corporation.

No person shall be elected by the stockholders as a Director of the Corporation unless nominated in accordance with the procedures set forth in this Section. Election of Directors at the annual meeting need not be by written ballot, unless otherwise provided by the Board of Directors or presiding officer at such annual meeting. If written ballots are to be used, ballots bearing the names of all the persons who have been nominated for election as Directors at the annual meeting in accordance with the procedures set forth in this Section shall be provided for use at the annual meeting.

Adopted and effective as of July 22, 2008

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