MEDNAX, INC. RESTRICTED SHARES UNITS AGREEMENT (this Agreement) FOR ROGER J. MEDEL, M.D. (the Recipient)

Exhibit 10.2

MEDNAX, INC.

RESTRICTED SHARES UNITS AGREEMENT

(this “Agreement”)

FOR

ROGER J. MEDEL, M.D.

(the “Recipient”)

1. Grant of Shares. The Compensation Committee (the “Committee”) of the Board of Directors of Mednax, Inc. (the “Company”) has granted on August 7, 2011 (the “Date of Grant”), to the Recipient, Eighty Seven Thousand One Hundred Sixty (87,160) Restricted Share Units pursuant to the Company’s 2008 Incentive Compensation Plan, as amended (the “Plan”), which is incorporated herein for all purposes and which shall control in the event of any conflict between any other provision of this Agreement. The Recipient hereby acknowledges receipt of a copy of the Plan and agrees to be bound by all of the terms and conditions hereof and thereof and all applicable laws and regulations. Unless otherwise provided herein, terms used herein that are defined in the Plan and not defined herein shall have the meanings attributed thereto in the Plan. Each Restricted Share Unit granted hereunder shall represent the right to receive one share of common stock, par value $.01 per share, of the Company and shall be for all purposes of the Plan, Deferred Stock.

2. Vesting of Restricted Share Units. Except as otherwise provided herein, the Restricted Share Units granted hereunder shall vest as provided below.

(a) Vesting After Satisfaction of Performance Criteria. Subject to the prior satisfaction of the performance criteria set forth in Section 10 of this Agreement, the Restricted Share Units shall vest upon the occurrence of any of the following:

(1) twenty-five percent (25%) of the Restricted Share Units shall vest upon the Committee’s certification that the Company’s income from operations, as determined in accordance with Generally Accepted Accounting Principles utilized by the Company in the preparation of its regularly prepared consolidated financial statements (such income from operations being referred to as “GAAP Income From Operations”), for any four consecutive fiscal quarters of the Company which elapse during the performance period described in Section 10(a) of this Agreement equals or exceeds $390,000,000;

(2) fifty percent (50%) of the Restricted Share Units (inclusive of any Restricted Share Units that have or would have vested pursuant to clause 1 above) shall vest upon the Committee’s certification that the Company’s GAAP Income From Operations for any four consecutive fiscal quarters of the Company which elapse during the performance period described in Section 10(a) of this Agreement equals or exceeds $430,000,000;

(3) seventy-five percent (75%) of the Restricted Share Units (inclusive of any Restricted Share Units that have or would have vested pursuant to clauses 1 and 2 above) shall vest upon the Committee’s certification that the Company’s GAAP Income From Operations for any four consecutive fiscal quarters of the Company which elapse during the performance period described in Section 10(a) of this Agreement equals or exceeds $475,000,000; and

(4) one-hundred percent (100%) of the Restricted Share Units (inclusive of any Restricted Share Units that have or would have vested pursuant to clauses 1, 2 and 3 above) shall vest upon the Committee’s certification that the Company’s GAAP Income From Operations for any four consecutive fiscal quarters of the Company which elapse during the performance period described in Section 10(a) of this Agreement equals or exceeds $525,000,000.

(b) Vesting in Connection with Certain Termination Events. (i) If the employment of Recipient is terminated pursuant to Section 4.2 [Disability], Section 4.3 [Death], Section 4.4 [Termination by

Employer Without Cause], Section 4.5 [Poor Health] or Section 4.7 [Termination by Employee for Good Reason] of the Employment Agreement, dated as of August 7, 2011 between the Recipient and Mednax Services, Inc. as in effect on the date hereof (the “Employment Agreement”), then the Restricted Share Units shall continue to vest in accordance with Section 2(a) of this Agreement notwithstanding the fact that such termination shall have occurred; or

(ii) If the employment of Recipient is terminated in circumstances in which Section 4.8 [Change in Control] of the Employment Agreement applies, then, irrespective of whether the performance criteria set forth in Section 10 of this Agreement have been satisfied, the Restricted Share Units shall automatically vest in full upon the date that such termination of employment is effective.

(c) Unvested Restricted Share Units. As of December 31, 2018, any Restricted Share Units granted hereunder that are not then vested under subsections (a) or (b) above, and have not been forfeited as provided elsewhere in this Agreement, shall automatically and without notice terminate, be forfeited and become null and void.

3. Forfeiture of Restricted Share Units. If, prior to the vesting of the Restricted Share Units granted hereunder, the Recipient breaches Section 8 of the Employment Agreement during the Employment Period (as defined in the Employment Agreement), or is terminated pursuant to Section 4.1 [Termination for Cause] or 4.6 [Termination by Employee without Good Reason] of the Employment Agreement, all of the Restricted Share Units granted hereunder which have not vested at the time of such breach or termination, as the case may be, shall automatically and without notice terminate, be forfeited and become null and void.

4. Payment of Restricted Share Units. On or after the date on which the Restricted Share Units granted hereunder vest pursuant to Section 2 above, and subject to compliance with Section 5 below, the Company shall promptly (and within two and one half (2 1/2) months after the Restricted Share Units vest) cause a certificate or certificates to be issued for and with respect to all of the shares of common stock of the Company underlying said Restricted Share Units issued to the Recipient. Any certificate(s) issued to evidence those shares shall bear those legends and endorsements that the Company shall deem necessary or appropriate (including those relating to restrictions on transferability and/or obligations and restrictions under the Securities Laws).

5. Tax Matters. The Recipient shall, no later than ten (10) business days from the date as of which the Restricted Share Units granted hereunder vest, pay to the Company, or make arrangements satisfactory to the Company for payment of, any federal, state or local taxes of any kind required by law to be withheld with respect to the Restricted Share Units granted hereunder (including without limitation the vesting thereof). If the Recipient fails to comply with the tax obligations set forth in the immediately preceding sentence (the “Tax Obligations”), then the Recipient hereby irrevocably authorizes and instructs a broker to be designated by the Company in its sole discretion to sell for the account of the Recipient a sufficient number of shares underlying the Restricted Share Units (based upon prevailing market prices at the time of such sale) necessary to satisfy the Recipient’s Tax Obligations, to remit to the Company the proceeds of such sale in such amount necessary to satisfy the Tax Obligations and to remit any balance resulting from such sale to the Recipient. In furtherance of the above, the Recipient hereby irrevocably authorizes the Company to instruct the transfer agent to transfer a portion of Recipient’s electronic shares to the designated broker in order to effectuate the sale of such shares required to satisfy the Recipient’s Tax Obligation. In addition, the Company shall, to the extent permitted by law, have the right to (a) deduct from any payment of any kind otherwise due to Recipient or (b) withhold and cancel an amount of shares of Company common stock underlying a vesting Restricted Share Unit having a Fair Market Value, as of the applicable vesting date equal to, any federal, state, or local taxes of any kind required by law to be withheld with respect to the Restricted Share Units (including without limitation the vesting thereof).

6. Non-Transferability of Restricted Share Units. The Restricted Share Units granted hereunder shall not be pledged, hypothecated or otherwise encumbered or subject to any lien, obligation or liability of the Recipient to any party (other than the Company or Related Entity), or assigned or transferred by the Recipient otherwise than by will or the laws of descent and distribution or to a Beneficiary upon the death of the Recipient. A Beneficiary or other person claiming any rights under the Plan or this Agreement from or through the Recipient shall be subject to all of the terms and conditions of the Plan and this Agreement, except as otherwise determined by the Committee, and to any additional terms and conditions deemed necessary or appropriate by the Committee. The transfer by the

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Recipient to a trust created by the Recipient for the benefit of the Recipient or the Recipient’s family which is revocable at any and all times during the Recipient’s lifetime by Recipient (unless Recipient becomes incapacitated) and as to which the Recipient is the sole trustee during his lifetime (unless Recipient becomes incapacitated and cannot serve as trustee) will not be deemed to be a transfer for purposes of this Section 6; provided, however, that no transfer to such trust shall preclude the forfeiture of the Restricted Share Units granted hereunder under the provisions of Section 2(a) or Section 3 or Section 10 of this Agreement.

7. Amendment, Modification & Assignment; Non-Transferability. This Agreement may only be modified or amended in a written document signed by the parties hereto. No promises, assurances, commitments, agreements, undertakings or representations, whether oral, written, electronic or otherwise, and whether express or implied, with respect to the subject matter hereof, have been made by either party which are not set forth expressly in this Agreement. The rights and obligations created hereunder shall be binding on the Recipient and his heirs and legal representatives and on the successors and assigns of the Company. Notwithstanding anything to the contrary in this Section 7, the parties shall not be permitted to modify or amend this Agreement if the effect of such modification or amendment would be to violate the anti-discretion requirements of Treasury Regulations Section 1.1 62-27(e)(2)(iii).

8. Complete Agreement. This Agreement (together with those agreements and documents expressly referred to herein, for the purposes referred to herein) embody the complete and entire agreement and understanding between the parties with respect to the subject matter hereof, and supersede any and all prior promises, assurances, commitments, agreements, undertakings or representations, whether oral, written, electronic or otherwise, and whether express or implied, which may relate to the subject matter hereof in any way.

9. Miscellaneous.

(a) No Right to Continued Employment or Service. This Agreement and the grant of Restricted Share Units hereunder shall not confer, or be construed to confer, upon the Recipient any right to employment or service, or continued employment or service, with the Company or any Related Entity.

(b) No Limit on Other Compensation Arrangements. Nothing contained in this Agreement shall preclude the Company or any Related Entity from adopting or continuing in effect other or additional compensation plans, agreements or arrangements, and any such plans, agreements and arrangements may be either generally applicable or applicable only in specific cases or to specific persons.

(c) Severability. If any term or provision of this Agreement is or becomes or is deemed to be invalid, illegal or unenforceable in any jurisdiction or under any applicable law, rule or regulation, then such provision shall be construed or deemed amended to conform to applicable law (or if such provision cannot be so construed or deemed amended without materially altering the purpose or intent of this Agreement and the grant of Restricted Share Units hereunder, such provision shall be stricken as to such jurisdiction and the remainder of this Agreement and the award hereunder shall remain in full force and effect).

(d) No Trust or Fund Created. Neither this Agreement nor the grant of Restricted Share Units hereunder shall create or be construed to create a trust or separate fund of any kind or a fiduciary relationship between the Company or any Related Entity and the Recipient or any other person. To the extent that the Recipient or any other person acquires a right to receive payments from the Company or any Related Entity pursuant to this Agreement, such right shall be no greater than the right of any unsecured general creditor of the Company.

(e) Law Governing. This Agreement shall be governed by and construed and enforced in accordance with the internal laws of the State of Florida (without reference to the conflict of laws rules or principles thereof).

(f) Interpretation. This Agreement is subject to all of the terms, conditions and provisions of the Plan, including, without limitation, the amendment provisions thereof, and to such rules, regulations and interpretations relating to the Plan adopted by the Committee as may be in effect from time to time. If and to the extent that the Agreement conflicts or is inconsistent with the terms, conditions and provisions of the Plan, the Plan

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shall control, and this Agreement shall be deemed to be modified accordingly. The Recipient accepts the Restricted Share Units granted hereunder subject to all of the terms, provisions and restrictions of this Agreement and the Plan. The undersigned Recipient hereby accepts as binding, conclusive and final all decisions or interpretations of the Board or the Committee upon any questions arising under this Agreement.

(g) Headings. Section, paragraph and other headings and captions are provided solely as a convenience to facilitate reference. Such headings and captions shall not be deemed in any way material or relevant to the construction, meaning or interpretation of this Agreement or any term or provision hereof.

(h) Notices. Any notice under this Agreement shall be in writing and shall be deemed to have been duly given when delivered personally or when deposited in the United States mail, registered, postage prepaid, and addressed, in the case of the Company, to the Company’s General Counsel at 1301 Concord Terrace, Sunrise, FL 33323 or if the Company should move its principal office, to such principal office, and, in the case of the Recipient, to the Recipient’s last permanent address as shown on the Company’s records, subject to the right of the Company to designate some other address at any time hereafter in a notice satisfying the requirements of this Section.

(i) Non-Waiver of Breach. The waiver by any party hereto of the other party’s prompt and complete performance, or breach or violation, of any term or provision of this Agreement shall be effected solely in writing signed by such party, and shall not operate nor be construed as a waiver of any subsequent breach or violation, and the waiver by any party hereto to exercise any right or remedy which he or it may possess shall not operate nor be construed as the waiver of such right or remedy by such party, or as a bar to the exercise of such right or remedy by such party, upon the occurrence of any subsequent breach or violation.

(j) Counterparts. This Agreement may be executed in two or more separate counterparts, each of which shall be an original, and all of which together shall constitute one and the same agreement.

10. Performance Awards. Notwithstanding anything in this Agreement to the contrary, the award of Restricted Share Units under Section 1, and the vesting of such award under Section 2, are intended to qualify as a “Performance Award” under Section 6(h) of the Plan. In furtherance of this intent, the following requirements shall be satisfied:

(a) Performance Period. The Committee has specified in accordance with Section 8(b) of the Plan that the “performance period” shall be the period commencing on October 1, 2011 and ending on December 31, 2018.

(b) Performance Criteria. The Committee has specified in accordance with Section 8(b) of the Plan that the performance criteria that must be met are as set forth in Section 2(a) of this Agreement .

(c) Vesting. All Restricted Share Units granted hereunder shall vest as specified in Section 2 of this Agreement.

(d) Further Steps. The Committee shall take all other steps as may be necessary under the Plan, and under Section 162 (m) of the Internal Revenue Code of 1986 (the “Code”) and the regulations thereunder to ensure that the award of Restricted Share Units, to the extent not otherwise forfeited under this Agreement, will be deductible by the Company under Code Section 162(m).

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IN WITNESS WHEREOF, the parties hereto, intending to be legally bound, have executed this Agreement as of the date first written above.

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