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 November 2004

                 (Translation of registrant's name into English)

                                  Canons Court
                               22 Victoria Street
                                 Hamilton HM 12
                    (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

                             Yes [_]    No [X]


            Attached hereto as Exhibit 1 is a copy of the press release issued
by Nordic American Tanker Shipping Limited ("NAT" or the "Company") on November
5, 2004, announcing a follow on offering of its common shares.

Exhibit 1

Nordic American Tanker Shipping Ltd. (NAT) - (AMEX: NAT) (OSE: NAT) Announces
Public Offering of Common Shares

Hamilton, Bermuda, November 5, 2004 --

Nordic American Tanker Shipping Ltd. (the "Company")  today announced that it is
commencing a public offering of 2,700,000 common shares.  The common shares will
be offered  pursuant to the Company's  effective shelf  registration  statement.
Bear,  Stearns & Co. Inc. and UBS Investment Bank will act as joint  bookrunning
managers and DnB NOR Markets,  Inc. will act as a  co-manager.  The Company will
grant the underwriters an option to purchase an additional 405,000 common shares
to cover any over-allotments, exercisable within 30 days.

The net  proceeds of this  offering  will be used to repay any amounts  borrowed
under the Company's senior secured credit facility to finance the acquisition of
a Suezmax  tanker  that the  Company  has  agreed to  purchase  and for  general
corporate purposes, including any future vessel acquisitions.

This press release shall not constitute an offer to sell or the  solicitation of
an offer to buy nor shall there be any sale of these  securities in any state in
which such offer,  solicitation  or sale would be unlawful prior to registration
or qualification under the securities laws of any state.

The offering will be made only by means of a prospectus  and related  prospectus
supplement.  A prospectus and the related  prospectus  supplement related to the
offering  will be filed  with  the  Securities  and  Exchange  Commission.  When
available,  copies of the  prospectus  relating to the  offering may be obtained
from the offices of Bear,  Stearns & Co. Inc. at 383 Madison  Avenue,  New York,
New York 10179, Attention:  Prospectus Department and UBS Investment Bank at 299
Park Avenue, New York, New York 10171, Attention: Syndicate Desk.

The  Company  is  an  international   tanker  company  that  owns  three  modern
double-hull  Suezmax tankers.  The Company expects to take delivery of the newly
acquired  Suezmax tanker in late November 2004. The Company operates its vessels
on bareboat, time and voyage charters.


Matters   discussed  in  this  press  release  may  constitute   forward-looking
statements.  The Private Securities  Litigation Reform Act of 1995 provides safe
harbor  protections  for  forward-looking   statements  in  order  to  encourage
companies   to   provide   prospective   information   about   their   business.
Forward-looking  statements  include  statements  concerning plans,  objectives,
goals, strategies,  future events or performance, and underlying assumptions and
other statements, which are other than statements of historical facts.

The  Company  desires to take  advantage  of the safe harbor  provisions  of the
Private  Securities  Litigation  Reform  Act  of  1995  and  is  including  this
cautionary statement in connection with this safe harbor legislation.  The words
"believe,"  "anticipate,"  "intend," "estimate,"  "forecast," "project," "plan,"
"potential,"   "will,"  "may,"   "should,"   "expect,"   "pending"  and  similar
expressions identify forward-looking statements.

The  forward-looking  statements  in this press  release are based upon  various
assumptions,  many of which  are  based,  in  turn,  upon  further  assumptions,
including  without  limitation,   our  management's  examination  of  historical
operating  trends,  data  contained in our records and other data available from
third parties.  Although we believe 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,  we cannot assure you that we will achieve or accomplish
these expectations, beliefs or projections. We undertake no obligation to update
any forward-looking  statement,  whether as a result of new information,  future
events or otherwise.

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, general market conditions, including
fluctuations in charter rates and vessel values, changes in demand in the tanker
market,  as a result of changes in OPEC's petroleum  production levels and world
wide oil consumption and storage,  changes in our operating expenses,  including
bunker  prices,  drydocking  and  insurance  costs,  the market for our vessels,
availability of financing and  refinancing,  changes in  governmental  rules and
regulations or actions taken by regulatory authorities, potential liability from
pending or future  litigation,  general  domestic  and  international  political
conditions,  potential  disruption  of  shipping  routes  due  to  accidents  or
political  events,  vessels  breakdowns  and  instances of  off-hires  and other
important  factors  described  from  time to time in the  reports  filed  by the
Company with the  Securities and Exchange  Commission,  including the prospectus
and related prospectus supplement and our Annual Report on Form 20-F.

              Scandic American Shipping Ltd
              Manager for
              Nordic American Tanker Shipping Ltd.
              P.O Box 56
              3201 Sandefjord
              Tel: + 47 33 42 73 00 E-mail:

              Rolf Amundsen
              Chief Financial Officer
              Nordic American Tanker Shipping Ltd.
              Tel: +1 800 601 9079 or + 47 908 26 906
              Herbjorn Hansson
              Chairman & CEO
              Nordic American Tanker Shipping Ltd.
              Tel:  +1 866 805 9504 or + 47 901 46 291


     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.


Dated:  November 8, 2004                 By:/s/ Herbjorn Hansson
                                                Herbjorn Hansson
                                                President and
                                                Chief Executive Officer

01318.0002 #523564