Exhibit 32.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER

AND CHIEF FINANCIAL OFFICER PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

I, Michael Klayko, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that the Quarterly Report on Form 10-Q of Brocade Communications Systems, Inc. for the fiscal quarter ended January 29, 2011 fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and that information contained in such Quarterly Report on Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of Brocade Communications Systems, Inc.

Date: March 2, 2011

I, Richard Deranleau, certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that the Quarterly Report on Form 10-Q of Brocade Communications Systems, Inc. for the fiscal quarter ended January 29, 2011 fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and that information contained in such Quarterly Report on Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of Brocade Communications Systems, Inc.

Date: March 2, 2011