FORM 6-K
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                        REPORT OF FOREIGN PRIVATE ISSUER

                    Pursuant to Rule 13a-16 or 15d-16 of the
                         Securities Exchange Act of 1934

                         For the month of May 2004

                         Commission File Number: 0-30852

                          GRUPO FINANCIERO GALICIA S.A.

                          Galicia Financial Group S.A.
                 (Translation of registrant's name into English)

                            Tte. Gral. Juan D. Peron 456
                        (C1038AAJ) Buenos Aires, Argentina
                    (Address of principal executive offices)


Indicate by check mark whether the registrant files or will file annual reports
under cover of Form 20-F or Form 40-F.

                           Form 20-F  X        Form 40-F
                                     ---                 ---

Indicate by check mark whether by furnishing the information contained in this
Form, the registrant is also thereby furnishing the information to the
Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

                               Yes             No  X
                                   ---            ---

If "Yes" is marked, indicate below the file number assigned to the registrant in
connection with Rule 12g3-2(b): 82- ________



                                    FORM 6-K

                           Commission File No. 0-30852

   Month Filed                 Event and Summary                     Exhibit No.

   May 2004          Press release, dated May 12, 2004                  99.1
                     regarding the Registrant's reporting of
                     its financial results for its fiscal
                     quarter ended March 31, 2004.



                                   SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.

                                      GRUPO FINANCIERO GALICIA S.A. (Registrant)



    Date:  May 14, 2004               By: /s/ Antonio Garces
                                          --------------------------------------
                                          Name:  Antonio Garces
                                          Title: Chief Executive Officer