Exhibit 2.1

AMENDMENT AND CONSENT TO AGREEMENT AND PLAN OF MERGER

This AMENDMENT AND CONSENT TO AGREEMENT AND PLAN OF MERGER (this “ Amendment and Consent ”), dated as of September 24, 2013, is entered into by and among Health Management Associates, Inc., a Delaware corporation (the “ Company ”), Community Health Systems, Inc., a Delaware corporation (“ Parent ”), and FWCT-2 Acquisition Corporation, a Delaware corporation (“ Merger Sub ”).

WHEREAS, the parties hereto are parties to the Agreement and Plan of Merger, dated as of July 29, 2013 (the “ Merger Agreement ”);

WHEREAS, the parties to the Merger Agreement desire to amend certain provisions thereof; and

WHEREAS, Parent and Merger Sub are agreeing to consent to certain actions for purposes of the Merger Agreement.

NOW, THEREFORE, in consideration of the foregoing and the mutual covenants and agreements herein contained, and intending to be legally bound hereby, the Company, Parent and Merger Sub hereby agree as follows (all capitalized terms used herein and not otherwise defined herein shall have the meanings ascribed to such terms in the Merger Agreement):

1. Amendments to the Merger Agreement .

(a) Section 5.02 of the Merger Agreement is hereby amended by inserting the following as a new subsection (j) thereof:

“Notwithstanding anything to the contrary contained in this Agreement, nothing contained in the Form S-4 (excluding, for purposes of this Section 5.02(j), any amendments or supplements thereto to the extent not approved by Parent) to be filed by Parent with the SEC substantially concurrently with the execution of this Amendment and Consent shall constitute a Company Adverse Recommendation Change for any purpose under this Agreement, including with respect to Parent’s rights under Section 8.01(f) and Section 8.03(b)(i) thereof.”

(b) Section 5.02 of the Merger Agreement is hereby amended by inserting the following as a new subsection (k) thereof:

“Notwithstanding anything to the contrary contained in this Agreement, the occurrence of any of the following events shall be deemed to be a Company Adverse Recommendation Change for all purposes under this Agreement, including with respect to Parent’s rights under Section 8.01(f) and Section 8.03(b)(i) thereof:

(i) Either of the Additional Financial Advisors shall have rendered an opinion containing any conclusion (A) that the Merger Consideration to be received by the holders of Company Common Stock in the Merger is other than

fair, from a financial point of view, to such holders (including, without limitation, any conclusion that the Merger Consideration is inadequate, grossly inadequate or any other similar conclusion) or (B) that is inconsistent in any respect with (1) the opinion, dated July 29, 2013, of Morgan Stanley & Co. LLC to the Company Board or (2) the Company Recommendation (disregarding any customary qualifications and disclaimers set forth in the opinion rendered by such Additional Financial Advisor); or

(ii) Either of the Additional Financial Advisors shall have been requested by the Company Board to render an opinion as to the fairness, from a financial point of view, of the Merger Consideration to be received by the holders of Company Common Stock in the Merger and such Additional Financial Advisor was unable or unwilling to conclude that the Merger Consideration to be received by the holders of Company Common Stock in the Merger is fair, from a financial point of view, to such holders.”

(c) Section 6.08 of the Merger Agreement is hereby amended by inserting the following as a new last sentence thereof:

“Notwithstanding anything to the contrary contained in this Agreement, Parent shall be given the opportunity to review and comment on any press release proposed to be issued by or on behalf of the Company, the Company Board or any committee thereof announcing, disclosing or otherwise mentioning the engagement of the Additional Financial Advisors, and no such press release shall be issued by or on behalf of the Company, the Company Board or any committee thereof without Parent’s prior written consent, which consent shall be at the sole discretion of Parent.”

(d) Section 9.03 of the Merger Agreement is hereby amended by inserting the following definitions in alphabetical order:

“Additional Financial Advisors” means Lazard Frères & Co. LLC and UBS Securities LLC.

“Definitive Proxy Statement” means a Proxy Statement forming a part of a Form S-4 that has been filed with the SEC and declared effective under the Securities Act, and that has been disseminated to stockholders of the Company.

(e) Section 6.01(b) of the Merger Agreement is hereby amended by adding the following proviso to the end thereof:

“; provided further, that in no event shall the Company Stockholders Meeting be held on, adjourned, recessed or postponed to a date that is on or after the third Business Day prior to the End Date without Parent’s prior written consent.”

2. Notification of Certain Matters . From and after the date of this Amendment and Consent until the earlier of the termination of the Merger Agreement and the Effective Time, the Company shall promptly (and in any event within 48 hours) notify Parent of the occurrence of any event described in Section 1(b)(i) or Section 1(b)(ii) of this Amendment and Consent.

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3. Consent to Engagement of Additional Financial Advisors .

(a) Notwithstanding anything to the contrary contained in the Merger Agreement, including Sections 3.25 and 5.01 thereof, each of Parent and Merger Sub hereby grants its consent to the engagement by the Company of each of the Additional Financial Advisors, solely upon the terms and subject to the conditions set forth in the Engagement Letters (the “Engagement Letters”) to be dated substantially concurrent with the execution of this Agreement and Consent between the Company and the Additional Financial Advisors, in each case in the form last provided to Parent prior to execution of this Amendment and Consent.

(b) As a condition to the consent set forth in this Section 3, the Company hereby represents, warrants and agrees that (i) except as expressly set forth in the Engagement Letters, there are and shall be no agreements or arrangements between, on behalf of, or otherwise binding upon (x) the Company, the Company Board or any committee thereof, on the one hand, and either Additional Financial Advisor or any of their respective Affiliates, on the other hand, or (y) to the Company’s knowledge following due inquiry, Glenview Capital Management, L.P. or any of its affiliated funds, on the one hand, and either Additional Financial Advisor or any of their respective Affiliates, on the other hand, solely for purposes of this clause (y), relating to the Merger or the matters for which the Additional Financial Advisors have been retained by the Company, and (ii) the Engagement Letters shall not be amended or otherwise modified in any respect (including, without limitation, by entering into any other agreements or arrangements with such Additional Financial Advisor that would otherwise be permitted by the terms of the Merger Agreement) without Parent’s prior written consent, which consent shall be at the sole discretion of Parent.

(c) The Company agrees that, if either of the Additional Financial Advisors shall have been or shall be requested to render an opinion as to the fairness, from a financial point of view, of the Merger Consideration to be received by the holders of Company Common Stock in the Merger, such opinion shall be made so that the Company shall be able to include the opinion and any disclosures relating thereto in the Definitive Proxy Statement; provided, however, that in no event shall such opinion be rendered later than November 19, 2013.

4. Representations and Warranties of the Company .

(a) The Company has all requisite corporate power and authority to execute and deliver this Amendment and Consent, to perform its obligations hereunder and to consummate the transactions contemplated by this Amendment and Consent.

(b) The Company has duly executed and delivered this Amendment and Consent and, assuming the due authorization, execution and delivery by Parent and Merger Sub, this Amendment and Consent constitutes its legal, valid and binding obligation, enforceable against it in accordance with its terms except as enforcement may be limited by bankruptcy, insolvency, reorganization or similar laws affecting creditors’ rights generally and by general principles of equity.

(c) The execution, delivery and performance by the Company of this Amendment and Consent and the consummation of the transactions contemplated hereby do not

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and will not (i) contravene, conflict with, or result in any violation or breach of any provision of the Company Charter, the Company By-laws or the comparable organizational documents of the Subsidiaries of the Company or (ii) contravene, conflict with or result in any violation or breach of any provision of any Applicable Law applicable to the Company or any Subsidiary of the Company or by which any property or asset of the Company or any Subsidiary of the Company is bound or affected.

5. Representations and Warranties of Parent and Merger Sub.

(a) Each of Parent and Merger Sub has all requisite corporate power and authority to execute and deliver this Amendment and Consent, to perform its obligations hereunder and to consummate the transactions contemplated by this Amendment and Consent.

(b) Each of Parent and Merger Sub has duly executed and delivered this Amendment and Consent and, assuming the due authorization, execution and delivery by the Company, this Amendment and Consent constitutes its legal, valid and binding obligation, enforceable against it in accordance with its terms except as enforcement may be limited by bankruptcy, insolvency, reorganization or similar laws affecting creditors’ rights generally and by general principles of equity.

(c) The execution, delivery and performance by each of Parent and Merger Sub of this Amendment and Consent and the consummation of the transactions contemplated hereby do not and will not (i) contravene, conflict with, or result in any violation or breach of any provision of the Parent Charter or the Parent By-laws or the certificate of incorporation or by-laws of Merger Sub or (ii) contravene, conflict with or result in any violation or breach of any provision of any Applicable Law applicable to Parent or Merger Sub or by which any property or asset of Parent or Merger Sub is bound or affected.

6. Effectiveness; No Waiver or Consent .

(a) The amendments set forth in this Amendment and Consent shall be effective immediately on the date hereof.

(b) Except as expressly amended by this Amendment and Consent, all other provisions of the Merger Agreement (including, without limitation, Section 5.02 thereof [ No Solicitation by the Company; Company Recommendation ]) shall be unchanged and remain in full force and effect, including, without limitation, the required or expected timing of any obligations of Parent, Merger Sub or the Company under the Merger Agreement. Without limiting the generality of the foregoing, the execution, delivery and performance of this Amendment and Consent shall not in any way affect the Company’s obligations to (i) prepare the Proxy Statement and cause it to be filed with the SEC as promptly as reasonably practicable after the execution of the Merger Agreement, (ii) use its reasonable best efforts to respond as promptly as reasonably practicable to any comments received from the SEC concerning the Proxy Statement and to resolve such comments with the SEC, (iii) use its reasonable best efforts to cause the Proxy Statement to be disseminated to its stockholders as promptly as reasonably practicable after the resolution of any comments received from the SEC concerning the Proxy Statement and (iv) take all necessary actions to duly call, give notice of, convene and hold the Company Stockholders Meeting as soon as reasonably practicable after the SEC confirms that it has no further comments on the Proxy Statement.

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(c) The execution, delivery and performance of this Amendment and Consent shall not, except as expressly provided herein, constitute a waiver of any provision of, operate as a waiver of any obligation, right, power or remedy of the parties hereto under, or constitute a consent to any action for purposes of, the Merger Agreement.

7. Interpretation. For the avoidance of doubt, from and after the date of this Amendment and Consent, references in the Merger Agreement to the “Agreement” or any provision thereof shall be deemed to refer to the Merger Agreement or such provision as amended hereby (unless the context otherwise requires) and references in the Merger Agreement to the “date hereof” or the “date of this Agreement” shall be deemed to refer to July 29, 2013. References in this Amendment and Consent to “the date hereof” refer to September 24, 2013 .

8. Counterparts . This Amendment and Consent may be executed in counterparts, including by facsimile or by email with .pdf attachments, all of which shall be considered one and the same agreement, and shall become effective when all counterparts have been signed by the parties and delivered to the other parties.

9. Entire Agreement; No Third-Party Beneficiaries . This Amendment and Consent constitutes the entire agreement, and supersedes all other prior agreements and understandings, both written and oral, among the parties and their Affiliates, or any of them, with respect to the subject matter hereof, and are not intended to and shall not confer upon any person other than the parties hereto, any rights or remedies hereunder.

10. Governing Law; Jurisdiction; Waiver of Jury Trial .

(a) This Amendment and Consent and all claims, actions, proceedings or counterclaims (whether based on contract, tort or otherwise) arising out of or relating to this Amendment and Consent, any of the transactions contemplated by this Amendment and Consent or the actions of Parent, Merger Sub or the Company in the negotiation, administration, performance and enforcement hereof and thereof, shall be governed by, and construed in accordance with, the laws of the State of Delaware (without giving effect to choice of law principles thereof).

(b) Each of the parties hereto (i) irrevocably consents to submit itself to the exclusive jurisdiction of the Delaware Courts in the event any dispute, claim or cause of action arises out of or relates to this Amendment and Consent or the transactions contemplated by this Amendment and Consent, (ii) agrees that it will not attempt to deny or defeat such personal jurisdiction by motion or other request for leave from any Delaware Court and (iii) agrees that it will not bring any claim or action arising out of or relating to this Amendment and Consent or the transactions contemplated by this Amendment and Consent in any court other than a Delaware Court. Each of the parties hereto hereby irrevocably and unconditionally consents to service of process in the manner provided for notices in Section 9.02 of the Merger Agreement. Nothing in this Amendment and Consent will affect the right of any party to this Amendment and Consent to serve process in any other manner permitted by Law.

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(c) EACH PARTY ACKNOWLEDGES AND AGREES THAT ANY CONTROVERSY WHICH MAY ARISE UNDER THIS AMENDMENT AND CONSENT IS LIKELY TO INVOLVE COMPLICATED AND DIFFICULT ISSUES, AND THEREFORE EACH SUCH PARTY HEREBY IRREVOCABLY AND UNCONDITIONALLY WAIVES ANY RIGHT SUCH PARTY MAY HAVE TO A TRIAL BY JURY IN RESPECT OF ANY LITIGATION DIRECTLY OR INDIRECTLY ARISING OUT OF OR RELATING TO THIS AMENDMENT AND CONSENT OR THE TRANSACTIONS CONTEMPLATED HEREBY, INCLUDING ANY CONTROVERSY INVOLVING ANY REPRESENTATIVE OF PARENT OR THE COMPANY UNDER THIS AMENDMENT AND CONSENT. EACH PARTY CERTIFIES AND ACKNOWLEDGES THAT (I) NO REPRESENTATIVE, AGENT OR ATTORNEY OF ANY OTHER PARTY HAS REPRESENTED, EXPRESSLY OR OTHERWISE, THAT SUCH OTHER PARTY WOULD NOT, IN THE EVENT OF LITIGATION, SEEK TO ENFORCE THE FOREGOING WAIVER, (II) EACH PARTY UNDERSTANDS AND HAS CONSIDERED THE IMPLICATIONS OF THIS WAIVER, (III) EACH PARTY MAKES THIS WAIVER VOLUNTARILY, AND (IV) EACH PARTY HAS BEEN INDUCED TO ENTER INTO THIS AMENDMENT AND CONSENT BY, AMONG OTHER THINGS, THE MUTUAL WAIVERS AND CERTIFICATIONS IN THIS SECTION 10.

[ Signature page follows. ]

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IN WITNESS WHEREOF, the Company, Parent and Merger Sub have duly executed this Amendment and Consent, all as of the date first written above.

[ Signature Page to Amendment and Consent to Agreement and Plan of Merger ]

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