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 September 2005

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

                               Tuborg Havnevej 18
                                DK-2900 Hellerup
                                     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 Share Statement No. 5 -
2005 issued by A/S STEAMSHIP COMPANY TORM to The Copenhagen Stock Exchange on
September 5, 2005.





Exhibit 1


SHARE STATEMENT No. 5 - 2005



05 September 2005



According to section 28a of the Danish Securities Trading Act, TORM must report
transactions made by senior staff and related parties in TORM's shares and
related securities:


Name                     Senior Vice President Kim Rasmussen
----                     -----------------------------------

Reason                   Other senior managers
Issuer                   A/S Dampskibsselskabet TORM
Securities code          DK0010281468
Name/description         Shares
Transaction              Sale
Trade date               02.09.2005
Market                   Copenhagen Stock Exchange
Number                   225
Market value in DKK      78,300




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: September 6, 2005
                                                     By: /s/ Klaus Nyborg
                                                     --------------------------
                                                     Klaus Nyborg
                                                     Chief Financial Officer








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