FORM 6-K

                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

                        Report of Foreign Private Issuer
                        Pursuant to Rule 13a-16 or 15d-16
                    under the Securities Exchange Act of 1934

                           For the month of March, 2004

                        Commission File Number 001-13896



                             Elan Corporation, plc
                 (Translation of registrant's name into English)


                Lincoln House, Lincoln Place, Dublin 2, Ireland
                    (Address of principal executive offices)



     Indicate  by check mark  whether the  registrant  files or will file annual
reports under cover of Form 20-F or Form 40-F:

                       Form 20-F /X/              Form 40-F / /


     Indicate  by check mark if the  registrant  is  submitting  the Form 6-K in
paper as permitted by Regulation S-T Rule 101(b)(1):

                             Yes / /                     No /X/

     Note: Regulation S-T Rule 101(b)(1) only permits the submission in paper of
a Form 6-K if submitted  solely to provide an attached annual report to security
holders.


     Indicate  by check mark if the  registrant  is  submitting  the Form 6-K in
paper as permitted by Regulation S-T Rule 101(b)(7):

                             Yes / /                     No /X/




                                      -2-


     Note: Regulation S-T Rule 101(b)(7) only permits the submission in paper of
a Form  6-K if  submitted  to  furnish  a  report  or  other  document  that the
registrant foreign private issuer must furnish and make public under the laws of
the jurisdiction in which the registrant is  incorporated,  domiciled or legally
organized  (the  registrant's  "home  country"),  or under the rules of the home
country exchange on which the registrant's securities are traded, as long as the
report or other document is not a press  release,  is not required to be and has
not been distributed to the registrant's  security holders, and, if discussing a
material  event,  has already been the subject of a Form 6-K submission or other
Commission filing on EDGAR.

     Indicate by check mark whether by furnishing the  information  contained in
this Form,  the  registrant 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/


     If  "Yes"  is  marked,  indicate  below  the file  number  assigned  to the
registrant in connection with Rule 12g3-2(b):






                                  EXHIBIT LIST


       Exhibit          Description
         99.1           Press release dated March 4, 2004 titled:
                        Elan to present at the SG Cowen 24th Annual Healthcare
                        Conference









                                   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.



                                              ELAN CORPORATION, plc



                                              By:   /s/ William F. Daniel
                                                        William F. Daniel
                                                        Company Secretary

Date: March 4, 2004