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 1934.

                                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 1,
2004, announcing the acquisition of a new vessel.

Exhibit 1

Nordic American  Tanker  Shipping Ltd. (NAT) - (AMEX:  NAT) (OSE: NAT) Announces
Vessel Acquisition

Hamilton, Bermuda, November 1, 2004

Nordic American  Tanker  Shipping Ltd. (the "Company")  today announced that the
Company has agreed to acquire the 149,591 dwt Suezmax  tanker M.T. Wilma Yangtze
from the Anders  Wilhelmsen group of Norway.  This tanker was built in China and
has been owned by Anders  Wilhelmsen  since it was  delivered  from the builder.
Following this acquisition,  the Company will have four environmentally friendly
modern  suezmax  oil  tankers.  All four  ships were built in 1997 and they have
double hull.

The Company's Chairman and CEO, Herbjorn Hansson,  commented:  "This transaction
is in line  with our  growth  strategy  of  accretive  acquisitions  to  bolster
dividends and earnings per share. I am pleased that we have been able to do this
business  which,  we  believe,  represents  an  important  step  in the  further
expansion of our Company - a process that we expect will continue."

The  acquisition  price for the ship of $66 million  will be financed  with a
revolving  credit  facility of $300 million that the Company has  established
with an international banking syndicate,  giving the Company important financial
flexibility  in the time to come. The Company will take over the ship at the end
of November and it will be bareboat  chartered  back to the present  owner until
the end of January  2005 at an average  rate of  approximately  $50,000  per day
(time charter equivalent).  Thereafter, the vessel is expected to be employed in
the spot market, technically and commercially under the control of the Company.


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," "except," "anticipate," "intends," "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.

In addition to these important  factors,  other  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 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

                     Gary J. Wolfe, Esq.
                     Seward & Kissel LLP, New York, USA
                     Tel: +1 212  574 1223

                     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 1, 2004                        By:/s/ Herbjorn Hansson
                                                       Herbjorn Hansson
                                                       President and
                                                       Chief Executive Officer

01318.0002 #522393