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 August 2004

                           A/S STEAMSHIP COMPANY TORM
                 (Translation of registrant's name into English)

                                   Marina Park
                                Sundkrogsgade 10
                              DK-2100 Copenhagen 0
                                     Denmark
                    (Address of principal executive offices)

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

                    Form 20-F [X]           Form 40-F [_]

        Indicate by check mark whether the registrant by furnishing the
information contained in this Form 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]




                  INFORMATION CONTAINED IN THIS FORM 6-K REPORT

     Set forth herein as Exhibit 1 is a copy of a Share Statement No. 13 - 2004
issued by A/S STEAMSHIP COMPANY TORM to The Copenhagen Stock Exchange on August
16, 2004





Exhibit 1
---------


SHARE STATEMENT No. 13 - 2004


16 August 2004




This is to notify you of changes in the shareholdings of the company's insiders
pursuant according to the Danish Securities Trading Act.



Securities    Trade      Holding    Market      Total Holding    Total market
code          date       number     value          number          value
----          ----       ------     -----          ------          -----

DK0010281468  12.08.2004 +1,600    243,200.00    2,363,366       357,128,192.00



A/S Dampskibsselskabet TORM
Contact person:   Klaus Nyborg, CFO (tel.: +45 39 17 92 00)







                                   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.

                           A/S STEAMSHIP COMPANY TORM
                                  (registrant)



Dated: August 18, 2004                           By: /s/ Klaus Nyborg
                                                    --------------------------
                                                  Klaus Nyborg
                                                  Chief Financial Officer

03810.0001 #506744