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 February 2004

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

                                   Marina Park
                                Sundkrogsgade 10
                              DK-2100 Copenhagen 0
                    (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|


          Set forth herein as Exhibit 1 is a copy of an Announcement No. 02 -
2004 issued by A/S STEAMSHIP COMPANY TORM to The Copenhagen Stock Exchange on
February 18, 2004.

Exhibit 1



                                                     A/S Dampskibsselskabet TORM
                                                     Marina Park
                                                     Sundkrogsgade 10
                                                     DK-2100 Copenhagen 0

18 February 2004

TORM places order for one more new-building and purchases second hand tanker

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

     o    The vessel is due to be delivered in 1st quarter 2008 and represents
          the latest addition to the substantial new-building program initiated
          in 1999. The six remaining new-buildings will be delivered in 2004-8
          and represent an investment of more than USD 200 mill.

     o    TORM has also signed a contract to acquire the 1995-built MR product
          tanker TORM ALICE from Rederi AB Gotland. The vessel, which is trading
          in TORM's MR pool, was owned by TORM until 2002 and will be delivered
          on 18 February 2004.

     o    The two transactions underline 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 and 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)
                    Klaus Nyborg, CFO (tel.: +45 39 17 92 00)

Matters discussed in this release may constitute forward-looking statements.
Forward-looking statements reflect our current views with respect to future
events and financial performance and may include statements concerning plans,
objectives, goals, strategies, future events or performance, and underlying
assumptions and other statements, which are other than statements of historical

The forward-looking statements in this release are based upon various
assumptions, many of which are based, in turn, upon further assumptions,
including without limitation, management's examination of historical operating
trends, data contained in our records and other data available from third
parties. Although TORM believes that these assumptions were reasonable when
made, because these assumptions are inherently subject to significant
uncertainties and contingencies which are difficult or impossible to predict and
are beyond our control, TORM cannot assure you that it will achieve or
accomplish these expectations, beliefs or projections.

Important factors that, in our view, could cause actual results to differ
materially from those discussed in the forward-looking statements include the
strength of world economies and currencies, changes in charter hire rates and
vessel values, changes in demand for "tonne miles" of crude oil carried by oil
tankers, the effect of changes in OPEC's petroleum production levels and
worldwide oil consumption and storage, changes in demand that may affect
attitudes of time charterers to scheduled and unscheduled drydocking, changes in
TORM's operating expenses, including bunker prices, dry-docking and insurance
costs, changes in governmental rules and regulations including requirements for
double hull tankers or actions taken by regulatory authorities, potential
liability from pending or future litigation, domestic and international
political conditions, potential disruption of shipping routes due to accidents
and political events or acts by terrorists.

Risks and uncertainties are further described in reports filed by TORM with the
US Securities and Exchange Commission, including the TORM Annual Report on Form
20-F and its reports on Form 6-K.


          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

Dated: February 23, 2004                         By: /s/ Klaus Nyborg
                                                     Klaus Nyborg
                                                     Chief Financial Officer

03810.0001 #465956