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 March 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. 1 - 2005
issued by A/S STEAMSHIP COMPANY TORM (the "Company") to The Copenhagen Stock
Exchange (the "Exchange") on March 9, 2005 and as Exhibit 2 is a copy of Share
Statement No. 2 - 2005 issued by the Company to the Exchange on March 10, 2005.



Exhibit 1

SHARE STATEMENT No. 1 - 2005


9 March 2005




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

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

DK0010281468   08.03.2005   -1,000  292,500.00    2,338,380     675,253,760.00


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



Exhibit 2


SHARE STATEMENT No. 2 - 2005



10 March 2005




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

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

DK0010281468   09.03.2005   +523     149,055.00    2,338,903    675,194,368.00



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: March 15, 2005
                                                   By: /s/ Klaus Nyborg
                                                   --------------------------
                                                   Klaus Nyborg
                                                   Chief Financial Officer


03810.0001 #555694