EXHIBIT 32.1

CERTIFICATION PURSUANT TO

SECTION OF 906 OF THE SARBANES-OXLEY ACT OF 2002

(18 U.S.C. SECTION 1350)

In connection with the Annual Report of Texas Industries, Inc. (the “Company”) on Form 10-K for the period ended May 31, 2010 (the “Report”), I, Mel G. Brekhus, President and Chief Executive Officer of the Company, hereby certify that to my knowledge:

(1) The Report 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 Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: July 21, 2010

A signed original of this written statement required by Section 906 has been provided to Texas Industries, Inc. and will be retained by Texas Industries, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.