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 this Annual Report of Burke & Herbert Financial Services Corp. (“Burke & Herbert”) on Form 10-K for the year ending December 31, 2023 as filed with the Securities and Exchange Commission on the date hereof, I, David P. Boyle, Chairman of the Board, President & Chief Executive Officer of Burke & Herbert, certify pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

(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 Form 10-K fairly presents, in all material respects, the financial condition and results of operations of Burke & Herbert.

By:	/s/ David P. Boyle
Name:	David P. Boyle
Title:	Chairman of the Board, President, & Chief Executive Officer

Date: March 22, 2024