EXHIBIT 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report on Form 10-Q of Select Medical Holdings Corporation (the “Company”) for the period ended September 30, 2024 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), we, David S. Chernow and Michael F. Malatesta, Chief Executive Officer and Chief Financial Officer, respectively, of the Company, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to our knowledge:

(1)    The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2)    The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company as of the dates and for the periods expressed in the Report.

October 31, 2024

/s/ David S. Chernow

David S. Chernow

Chief Executive Officer

/s/ Michael F. Malatesta

Michael F. Malatesta

Executive Vice President and Chief Financial Officer