Exhibit 32.1

Certification of Periodic Report Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

     For the purpose of 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned, Laurence E. Hirsch, the Chief Executive Officer of Centex Construction Products, Inc. (the “Company”), hereby certifies that, to his knowledge:

(i)	the Quarterly Report on Form 10-Q of the Company for the quarter ended June 30, 2003, as filed with the Securities and Exchange Commission on the date hereof (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and
(ii)	the information contained in the Report fairly presents, in all material respects, the financial condition and results of operation of the Company.

Dated:	August 12, 2003
By:	/s/ LAURENCE E. HIRSCH Laurence E. Hirsch Chief Executive Officer

The foregoing certification is being furnished as an exhibit to the Form 10-Q pursuant to Item 
601(b)(32) of Regulation S-K and Section 906 of the Sarbanes-Oxley Act of 2002 and, accordingly,
is not being filed as part of the Form 10-Q.