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 June, 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        /X/          No       / /

     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     /X/             No      / /


                                      -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 June 3, 2004 titled:
                Elan announces webcast of annual general meeting
                on June 17, 2004.










                                   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: June 3, 2004






                                                                    Exhibit 99.1



                              FOR IMMEDIATE RELEASE



Investors:                                                Media:
Emer Reynolds                                             Anita Kawatra
Ph:      353-1-709-4000                                   Ph:  212-407-5755
         800-252-3526                                          800-252-3526


                ELAN ANNOUNCES WEBCAST OF ANNUAL GENERAL MEETING
                                on JUNE 17, 2004

DUBLIN, IRELAND, JUNE 3, 2004 -- Elan Corporation, plc announced today that its
annual general meeting (AGM) to be held on June 17, 2004 at 10.30am BST / 5.30am
ET in The Shelbourne Hotel, St Stephens Green, Dublin 2, Ireland will be
available by webcast. Live audio of the AGM will be broadcast over the Internet
and will be available to investors, members of the news media and general
public.

This event can be accessed by visiting Elan's website at www.elan.com and
clicking on the Investor Relations section, then on the event icon. The event
will be archived and available for replay at the same URL.

About Elan

Elan is focused on the discovery, development, manufacturing, sale and marketing
of novel therapeutic products in neurology, severe pain and autoimmune diseases.
Elan (NYSE: ELN) shares trade on the New York, London and Dublin Stock
Exchanges.