Tipperary (TPY) 10-Q 2004 Q2 Quarterly report

Exhibit 32.1

Certification of Chief Executive Officer
of Tipperary Corporation  Pursuant to 18 U.S.C. §1350

In connection with the Quarterly Report on Form 10-Q of Tipperary Corporation (the “Company”) for the period ended June 30, 2004, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, David L. Bradshaw, Chief Executive Officer of the Company, certify pursuant to 18 U.S.C. §1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to the best of 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.

	/s/ David L. Bradshaw
Name:		David L. Bradshaw
Title:		Chief Executive Officer
Date:		August 16, 2004