EXHIBIT 32.1

            SECTION 906 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, 2003 (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, 2003                     /s/ Timothy W. Byrne
                                             -----------------------------------
                                             Timothy W. Byrne
                                             President and Chief Executive
                                             Officer