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 May 1, 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 May 1, 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