EXHIBIT 32

                           CERTIFICATION PURSUANT TO
                            18 U.S.C. SECTION 1350,
                             AS ADOPTED PURSUANT TO
                 SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

    The following certification is being furnished solely to accompany the
Report pursuant to 18 U.S.C. 'SS'1350 and in accordance with SEC Release No.
33-8238. This certification shall not be deemed 'filed' for purposes of Section
18 of the Securities Exchange Act of 1934, as amended, nor shall it be
incorporated by reference in any filing of the Company under the Securities Act
of 1933, as amended, whether made before or after the date hereof, regardless of
any general incorporation language in such filing.

    In connection with the Annual Report of J. W. Mays, Inc. (the 'Company') on
Form 10-K for the period ending July 31, 2005 as filed with the Securities and
Exchange Commission (the 'Report'), we, Lloyd J. Shulman and Mark S. Greenblatt,
Chief Executive Officer and Chief Financial Officer, respectively, of the
Company, certify, pursuant to 18 U.S.C. 'SS'1350, as adopted pursuant to 'SS'906
of the Sarbanes-Oxley Act of 2002, that to our knowledge:

        (1) The Report fully complies with the requirements of Section 13(a) or
            15(d) of the Securities Exchange Act of 1934; and

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

October 13, 2005

                                             /s/ LLOYD J. SHULMAN
                                          --------------------------
                                             Lloyd J. Shulman
                                             Chief Executive Officer

                                             /s/ MARK S. GREENBLATT
                                          --------------------------
                                             Mark S. Greenblatt
                                             Chief Financial Officer

    A signed original of this written statement required by Section 906 has been
provided to J.W. Mays, Inc. and will be retained by J. W. Mays, Inc. and
furnished to the Securities and Exchange Commission or its staff upon request.