EXHIBIT 32.1

SECTION 1350 CERTIFICATION BY THE CHIEF EXECUTIVE OFFICER

     I, Timothy W. Byrne, Chief Executive Officer of United States Lime & Minerals, Inc. (the “Company”), hereby certify that, to my knowledge:

(1)	The Company’s periodic report on Form 10-Q for the quarterly period ended September 30, 2004 (the “Form 10-Q”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; 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: November 3, 2004	/s/ Timothy W. Byrne
	Timothy W. Byrne
	President and Chief Executive Officer