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
     March 31, 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:  May 11, 2004                 /s/ Timothy W. Byrne
                                     -----------------------------------------
                                         Timothy W. Byrne
                                         President and Chief Executive Officer