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, Gregory L. Reyes, 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 of Brocade Communications Systems, Inc. on Form 10-Q for the fiscal
quarter ended July 31, 2004 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.

                                           By:  /s/ Gregory L. Reyes
                                                --------------------------------
                                                Gregory L. Reyes
                                                Chairman of the Board and
                                                Chief Executive Officer

I, Antonio Canova, 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 of Brocade Communications Systems, Inc. on Form 10-Q for the fiscal
quarter ended July 31, 2004 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.

                                           By:  /s/ Antonio Canova
                                                --------------------------------
                                                Antonio Canova
                                                Vice President, Finance and
                                                Chief Financial Officer