
<PAGE>   1
 
                                                                      EXHIBIT 24
 
                               POWER OF ATTORNEY
 
     The undersigned officers and directors of GATX CORPORATION, a New York
corporation, do hereby constitute and appoint David B. Anderson and Ronald J.
Ciancio, or either of them, attorneys and agents of the undersigned, with full
power and authority to sign in the name and on behalf of the undersigned, and in
the capacities indicated, its registration statement on Form S-8 under the
Securities Act of 1933 of 200,000 shares of Common Stock to be purchased under
the GATX Logistics Inc., 401(k) Cash Accumulation Plan, together with any
amendments thereto, hereby ratifying and confirming all that said attorneys and
agents and each of them may do by virtue hereof.
 
<TABLE>
<CAPTION>
                   SIGNATURE                               TITLE                   DATE
- ------------------------------------------------     ------------------     ------------------
<C>                                                  <S>                    <C>
                ________________                     Director               June 19, 1996
                Franklin A. Cole
                 ______________                      Director               June 19, 1996
                 James M. Denny
                ________________                     Director               June 19, 1996
                William C. Foote
                _________________                    Director               June 19, 1996
                Deborah M. Fretz
                _________________                    Director               June 19, 1996
               Richard A. Giesen
                 ______________                      Director               June 19, 1996
                 Miles L. Marsh
                _________________                    Director               June 19, 1996
                Charles Marshall
               __________________                    Director               June 19, 1996
               Michael E. Murphy
                 _______________                     Chairman of the        June 19, 1996
                 Ronald H. Zech                        Board and Chief
                                                       Executive
                                                       Officer
</TABLE>
