Exhibit 32.1

Certification of

Chief Executive Officer

of First Financial Bankshares, Inc.

This certification is provided pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code) and accompanies the quarterly report on Form 10-Q (the “Form 10-Q”) for the quarter ended March 31, 2026 of First Financial Bankshares, Inc. (the “Company”).

I, David W. Bailey, the President and Chief Executive Officer of the Company, certify that:

1. the Form 10-Q fully complies with the requirements of section 13(a) or section 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m(a) or 78o(d)); and

2. the information contained in the Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: May 5, 2026

By:		/s/ David W. Bailey
		David W. Bailey
		President and Chief Executive Officer

Subscribed and sworn to before me this 5th day of May, 2026.

/s/ Melissa Ann Kampert

Melissa Ann Kampert

Notary Public

My commission expires: October 11, 2028