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         / /             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/




     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):







This Report of Foreign Issuer on Form 6-K is incorporated by reference into the
Post-Effective Amendments on Forms F-3 and S-8 to Form F-4 Registration
Statement of Elan Corporation, plc (Registration No. 333-12756), the
Registration Statement on Form F-3 of Elan Corporation, plc and Athena
Neuroscience Finance, LLC (Registration No. 333-13130), and the Registration
Statements on Form S-8 of Elan Corporation, plc (Registration Nos. 333-13996,
333-12344, 333-11940, 333-09644, 333-09284, 333-09048, 333-08384, 333-07361,
333-07136, 333-14240, 33-27506, 333-100252 and 333-100556).










                                  EXHIBIT LIST


   Exhibit      Description

     99.1       Press release dated June 4, 2004 titled:
                Biogen Idec and Elan submit application to the European
                Medicines Agency for approval of Antegren(R) for multiple
                sclerosis based on one-year data.








                                   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 4, 2004





                                                                    Exhibit 99.1



For More Information Contact:
MEDIA CONTACTS:
Biogen Idec                               Elan
Amy Brockelman                            Anita Kawatra
Ph: 617 914 6524                          Ph: 212 407 5755
                                          800 252 3526

INVESTOR CONTACTS:
Biogen Idec                               Elan
Elizabeth Woo                             Emer Reynolds
Ph: 617 679 2812                          Ph: 353 1 709 4000
                                          800 252 3526



             BIOGEN IDEC AND ELAN SUBMIT APPLICATION TO THE EUROPEAN
                MEDICINES AGENCY FOR APPROVAL OF ANTEGREN(R)FOR
                    MULTIPLE SCLEROSIS BASED ON ONE-YEAR DATA

Cambridge, MA, San Diego, CA and Dublin, Ireland - June 4, 2004 - Biogen Idec
(NASDAQ: BIIB) and Elan Corporation, plc (NYSE: ELN) announced today that they
have submitted a Marketing Authorisation Application (MAA) to the European
Medicines Agency for approval of ANTEGREN(R) (natalizumab) as a treatment for
multiple sclerosis (MS).

The submission includes one-year data from two ongoing Phase III trials. The
companies are committed to completing these two-year trials. In order to protect
the integrity of the trials, the companies are not disclosing the one-year data
at this time. Last month, Biogen Idec and Elan submitted a Biologics License
Application (BLA) to the U.S. Food and Drug Administration (FDA) for the
approval of natalizumab for MS.

"Based on the promising results in previous clinical trials and the one-year
analysis from our Phase III studies, we believe natalizumab has the potential to
meet a significant unmet need for MS patients around the world," said Burt
Adelman, MD, executive vice president, Development,



Biogen Idec. "Natalizumab's novel mechanism of action represents an innovative
approach to treating MS."

"This submission represents a significant milestone for Elan and Biogen Idec and
demonstrates our ongoing commitment to new therapies for MS patients," said Lars
Ekman, MD, executive vice president and president Research & Development, Elan.
"We will continue to work with European regulators during the review process to
bring natalizumab to patients as quickly as possible."

MS is a chronic disease of the central nervous system that affects approximately
400,000 people in Europe and approximately one million people worldwide. It is a
disease that affects more women than men, with onset typically between 20 and 40
years of age. Symptoms of MS may include vision problems, loss of balance,
numbness, difficulty walking and paralysis.

About the MS Clinical Trials for ANTEGREN

The AFFIRM (natalizumab safety and efficacy in relapsing-remitting MS) trial is
a two-year, randomized, multi-center, placebo-controlled, double-blind study of
approximately 900 patients, evaluating the ability of natalizumab to slow the
progression of disability in MS and reduce the rate of clinical relapses. The
SENTINEL (safety and efficacy of natalizumab in combination with AVONEX(R)
(Interferon beta-1a)) trial is a two-year, randomized, multi-center,
placebo-controlled, double-blind study of approximately 1,200 patients with
relapsing-remitting MS, evaluating the effect of the combination of natalizumab
and AVONEX compared to treatment with AVONEX alone in slowing the progression of
disability and reducing the rate of clinical relapses. Both study protocols
provided for a one-year analysis of the data. The primary endpoints for both
Phase III two-year trials in MS are based on the Expanded Disability Status
Scale (EDSS) and relapse rate. The pre-specified primary endpoint of the
one-year analysis was relapse rate.

About ANTEGREN (natalizumab)

Natalizumab, a humanized monoclonal antibody, is the first alpha-4 antagonist in
the new selective adhesion molecule (SAM) inhibitor class. The drug is designed
to inhibit the migration of immune cells into chronically inflamed tissue where
they may cause or maintain



inflammation. To date, approximately 2,800 patients have received natalizumab in
clinical trials, and the safety profile continues to support further
development. In placebo-controlled trials to date, in both Crohn's disease (CD)
and MS, the most commonly reported adverse events in either group were headache,
fatigue and nasopharyngitis.

Biogen Idec and Elan are collaborating equally on the development of natalizumab
in MS, CD, and rheumatoid arthritis (RA).


About Biogen Idec

Biogen Idec creates new standards of care in oncology and immunology. As a
global leader in the development, manufacturing, and commercialization of novel
therapies, Biogen Idec transforms scientific discoveries into advances in human
healthcare. For product labeling, press releases and additional information
about the company, please visit http://www.biogenidec.com.

About Elan

Elan Corporation, plc is a neuroscience-based biotechnology company that is
focused on discovering, developing, manufacturing and marketing advanced
therapies in neurology, autoimmune diseases, and severe pain. Elan shares trade
on the New York, London and Dublin Stock Exchanges. For additional information
about the company, please visit http://www.elan.com.

Safe Harbour/Forward Looking Statements

This press release contains forward-looking statements regarding the approval of
ANTEGREN (natalizumab) and the potential of natalizumab as a treatment for MS.
These statements are based on the companies' current beliefs and expectations.
Drug development involves a high degree of risk. Factors which could cause
actual results to differ materially from the companies' current expectations
include: the risk that unexpected concerns may arise from additional data or
analysis, that regulatory authorities may require additional information or
further studies or may fail to approve the drug, or that the companies may
encounter other unexpected hurdles. For more detailed information on the risks
and uncertainties associated with the companies' drug development and other
activities, see the periodic reports of Biogen Idec Inc. and Elan Corporation,
plc filed with the Securities and Exchange Commission. The companies assume no
obligation to update any forward-looking statements, whether as a result of new
information, future events or otherwise.

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