Exhibit 3.1

CERTIFICATE OF AMENDMENT
OF THE
CERTIFICATE OF INCORPORATION
OF
SELECT MEDICAL HOLDINGS CORPORATION

Pursuant to the provisions of Section 242 of the General Corporation Law of the State of Delaware (the “DGCL”), Select Medical Holdings Corporation, a corporation organized and existing under the laws of the State of Delaware (the “Corporation”), hereby certifies as follows:

1. The name of the Corporation is Select Medical Holdings Corporation. The date of the filing of its Certificate of Incorporation with the Secretary of State of the State of Delaware was October 14, 2004.

2. This Certificate of Amendment (this “Amendment”) amends provisions of the Certificate of Incorporation and has been duly adopted by the Board of Directors of the Corporation, declaring said amendment to be in the best interests of the Corporation and its stockholders, and authorizing the appropriate officers of the Corporation to solicit the consent of the stockholders thereof.

3. Article SEVENTH of the Certificate of Incorporation is hereby amended and restated in its entirety as follows

“SEVENTH: Bylaws. In furtherance and not in limitation of the powers conferred by statute, the Board is expressly authorized to make, alter, amend or repeal the Bylaws of the Corporation (the “Bylaws”) without the assent or vote of the stockholders of the Corporation. The stockholders may, at any annual or special stockholder meeting, duly called and upon proper notice thereof, make, alter, amend or repeal the Bylaws by the affirmative vote by the holders of not less than a majority of the Corporation’s outstanding shares.”

4. Article THIRTEENTH of the Certificate of Incorporation is hereby amended and restated in its entirety as follows

“THIRTEENTH: Amendments. The Corporation reserves the right to amend, alter, change or repeal any provisions contained in this Restated Certificate of Incorporation or any amendment thereof from time to time and at any time in the manner now or hereafter prescribed by statute, and all rights conferred upon stockholders herein are granted subject to this reservation; provided, however, that, notwithstanding anything to the contrary elsewhere contained in this Restated Certificate of Incorporation, Articles FIFTH, SIXTH, SEVENTH, EIGHTH, NINTH, TENTH, ELEVENTH, TWELFTH and THIRTEENTH shall not be amended, altered or repealed without the affirmative vote of the holders of not less than a majority of the Corporation’s outstanding shares.”

5. All other provisions of the Certificate of Incorporation shall remain in full force and effect.

[Signature Page Follows]

THIS CERTIFICATE OF AMENDMENT OF THE CERTIFICATE OF INCORPORATION is executed as of this 28th day of April, 2025.

[Signature Page to Certificate of Amendment]

Exhibit 3.2

SELECT MEDICAL HOLDINGS CORPORATION

AMENDMENT NO. 1

TO

AMENDED AND RESTATED BYLAWS

The Amended and Restated Bylaws of Select Medical Holdings Corporation, a Delaware corporation (the “Corporation”), are hereby amended by deleting therefrom Section 2.11 and Section 9.1 of the Amended and Restated Bylaws in their entirety and inserting the following in lieu thereof:

“Section 2.11 Removal of Directors. Any Director may be removed at any time, but only for cause upon the affirmative vote of the holders of a majority of the Corporation’s outstanding shares entitled to vote generally in the election of Directors at any meeting of such stockholders, including meetings called expressly for that purpose, and at which a quorum of stockholders is present. Subject to the rights of the holders of any series of preferred stock of the Corporation, any vacancy in the Board of Directors caused by any such removal shall be filled at such meeting by the stockholders entitled to vote for the election of the Director so removed.”

“Section 9.1        Amendment. Subject to any express provision in the Restated Certificate of Incorporation to the contrary, these Bylaws may be amended, altered or repealed:

(a)         by resolution adopted by a majority of the Board of Directors at any special or regular meeting of the Board of Directors without the assent or vote of the stockholders of the Corporation if, in the case of such special meeting only, notice of such amendment, alteration or repeal is contained in the notice or waiver of notice of such meeting; or

(b)         at any regular or special meeting of the stockholders upon the affirmative vote of not less than a majority of the Corporation’s outstanding shares entitled to vote generally in the election of Directors if, in the case of such special meeting only, notice of such amendment, alteration or repeal is contained in the notice or waiver of notice of such meeting.

Except as set forth in this Amendment No.1 to the Amended and Restated Bylaws of the Corporation, the Amended and Restated Bylaws of the Corporation shall continue in full force and effect without modification.

Effective: April 29, 2025

Exhibit 10.1

SELECT MEDICAL HOLDINGS CORPORATION

Non-Employee Director Compensation Policy

Effective Date: April 24, 2025

The purpose of this Policy of Select Medical Holdings Corporation (“Select Medical” or the “Company”), is to provide a total compensation package that enables the Company to attract and retain, on a long-term basis, high-caliber directors, who are not employees or officers of the Company or its subsidiaries (“Non-Employee Directors”), to serve on the Company’s Board of Directors (the “Board”).

In furtherance of the above, all Non-Employee Directors of Select Medical will receive the compensation described in this Director Compensation Policy (the “Director Compensation Policy”) for his or her Board service as set forth below, following the date of approval of the Director Compensation Policy by the Company’s stockholders (the “Effective Date”).

Each Non-Employee Director will receive the cash compensation set forth below for service on the Board or a committee of the Board. The annual cash compensation amounts will be payable in equal quarterly installments, each payment made in advance on the first business day of the quarterly period for which the service will occur. Any amount payable for a partial quarter of service in an applicable role will be pro-rated by multiplying such amount by a fraction, the numerator of which will be the number of days of service in such role that the Non-Employee Director provided in such quarter and the denominator of which will be the number of days in such quarter. All cash fees are vested upon payment.

$18,000 for general availability and participation in meetings and on conference calls of the Board of Directors.

a.             Member of Audit and Compliance Committee:

i. Attendance Fee Per In-Person Meeting (when held in conjunction with a Board meeting): $4,000

ii. Attendance Fee Per In-Person Meeting (when held independent of a Board meeting): $5,000

iii. Attendance Fee Per Telephonic Meeting: $2,000

b.             Nominating, Governance and Sustainability Committee:

i. Attendance Fee Per In-Person Meeting (when held in conjunction with a Board meeting): $1,500

ii. Attendance Fee Per In-Person Meeting (when held independent of a Board meeting): $2,000

iii. Attendance Fee Per Telephonic Meeting: $500

c.             Member of Human Capital and Compensation Committee:

i. Attendance Fee Per In-Person Meeting (when held in conjunction with a Board meeting): $1,500

ii. Attendance Fee Per In-Person Meeting (when held independent of a Board meeting): $2,000

iii. Attendance Fee Per Telephonic Meeting: $500

d.             Member of Quality of Care and Patient Safety Committee:

i. Attendance Fee Per In-Person Meeting (when held in conjunction with a Board meeting): $2,500

ii. Attendance Fee Per In-Person Meeting (when held independent of a Board meeting): $3,000

iii. Attendance Fee Per Telephonic Meeting: $1,000

e.             Other Committees: Compensation for other committees shall be determined by the Board of Directors.

a.             Chair of Audit and Compliance Committee:

i. Attendance Fee Per In-Person Meeting: $2,000

ii. Attendance Fee Per Telephonic Meeting: $1,000

b.             Chair of Nominating, Governance and Sustainability Committee:

i. Attendance Fee Per In-Person Meeting: $1,000

ii. Attendance Fee Per Telephonic Meeting: $500

c.             Chair of Human Capital and Compensation Committee:

i. Attendance Fee Per In-Person Meeting: $1,000

ii. Attendance Fee Per Telephonic Meeting: $500

d.             Chair of Quality of Care and Patient Safety Committee:

i. Attendance Fee Per In-Person Meeting: $2,000

ii. Attendance Fee Per Telephonic Meeting: $1,000

All grants of equity retainer awards to Non-Employee Directors pursuant to this Policy will be automatic and nondiscretionary and will be made in accordance with the following provisions:

Annual grants made on or after the annual meeting of the Company’s stockholders (the “Annual Meeting”) during 2025 (the “2025 Annual Meeting”) shall be made as follows:

The “RS Value” of a Continuing Director Annual RS Award or New Director RS Award shall reflect a sufficient number of Shares to be granted under this policy multiplied by the closing price of a Share on the stock exchange or a national market system on which the Shares are listed on the grant date, such that the RS Value equals $200,000; provided that the number of Shares covered by each Continuing Director Annual RS Award or New Director RS Award will be rounded to the nearest whole integer.

The remaining terms and conditions of each RS Award granted under this policy will be as set forth in the Plan and the Company’s standard form of RS Award agreement for Non-Employee Directors currently in effect, as it may be amended from time to time by the Board or the Compensation Committee of the Board, as applicable. If permitted by the Company, the issuance of the Shares issuable with respect to an RS Award may be deferred upon such terms and conditions as determined by the Company, subject to the Company’s determination that any such right of deferral or any term thereof complies with applicable laws or regulations in effect from time to time.

Expense Reimbursement. Each non-management board member shall be reimbursed for his or her reasonable out-of-pocket business expenses incurred in connection with attending meetings of the Board of Directors or its Committees or in connection with other Board related business.