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 Annual Report on Form 10-K for the year ended
                  December 31, 2003 (the "Form 10-K") 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-K fairly presents, in
                  all material respects, the financial condition and results of
                  operations of the Company.

Dated: March 29, 2004                     /s/ Timothy W. Byrne
                                          --------------------------------------
                                          Timothy W. Byrne
                                          President and Chief Executive Officer