Exhibit 32.1

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350

AS ADOPTED PURSUANT TO SECTION 906

OF THE SARBANES-OXLEY ACT OF 2002

I, Vivek Y. Ranadive, President and Chief Executive Officer of TIBCO Software Inc. (the “Company”), do hereby certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to my knowledge:

(a) the Quarterly Report on Form 10-Q of the Company for the fiscal quarter ended August 29, 2004, as filed with the Securities and Exchange Commission (the Report), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(b) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: October 13, 2004

/s/ Vivek Y. Ranadivé

Vivek Y. Ranadivé

President and Chief Executive Officer