Exhibit 32.1

              Certification of President and Chairman of the Board

  Pursuant to Section 1350 of Chapter 63 of Title 18 of the United States Code


         I,  William R. Thomas,  President  and Chairman of the Board of Capital
Southwest Corporation, certify that to my knowledge:

         1. the Form 10-K, filed with the Securities and Exchange  Commission on
June 11, 2004  ("accompanied  report") fully complies with the  requirements  of
Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

         2. the information contained in the accompanied report fairly presents,
in all material respects,  the consolidated  financial  condition and results of
operations of Capital Southwest Corporation.


                                             /s/ William R. Thomas
                                             -----------------------------------
                                             William R. Thomas
                                             President and Chairman of the Board
                                             June 11, 2004