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 October, 2003

                          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 Copenhagen Stock Exchange
Announcement No. 10 - 2003 issued by A/S STEAMSHIP COMPANY TORM to The
Copenhagen Stock Exchange on October 21, 2003.



Exhibit 1

COPENHAGEN STOCK EXCHANGE ANNOUNCEMENT NO.  10 - 2003

21 October 2003

TORM - places order for two more newbuildings

o    A/S Dampskibsselskabet TORM has signed a contract with Dalian New
     Shipbuilding Ltd. in the People's Republic of China for construction of
     two high specification 110,000 dwt Aframax (LR2) product tankers. This
     order is based on the two options granted when TORM placed the initial
     order for two vessels in June 2003. TORM has an option for a further two
     vessels.

o    The two vessels are due to be delivered in 1st and 2nd quarter 2007, and
     represent the latest additions to the substantial newbuilding programme
     initiated in 1999. The seven remaining newbuildings will be delivered in
     2003-7 and represent an investment of more than USD 250 mill.

o    This order underlines TORM's commitment to a strategy based on owning and
     operating, in cooperation with its pool partners, a product tanker fleet
     among the most modern and technologically advanced in the world, aimed at
     offering customers the capacity, flexibility and quality required.

A/S Dampskibsselskabet TORM
Contact person:   Klaus Kjaerulff, CEO (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: October 21, 2003                 By: /s/ Klaus Nyborg
                                        --------------------------------------
                                        Klaus Nyborg
                                        Chief Financial Officer

03810.0001 #437018