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 June 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. 4 - 2005
issued by A/S STEAMSHIP COMPANY TORM to The Copenhagen Stock Exchange on May 31,
2005.




Exhibit 1
---------


SHARE STATEMENT No. 4 - 2005


31 May 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                   Klaus Nyborg

 Reason                  CFO
 Issuer                  A/S Dampskibsselskabet TORM
 Securities code         DK0010281468
 Name/description        Shares
 Transaction             Sale
 Trade date              30.05.2005
 Market                  Copenhagen Stock Exchange
 Number                  2,500
 Market value in DKK     800,000.00


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



03810.0001 #576901