<PAGE>   1
      As filed with the Securities and Exchange Commission on May 25, 2000

                                                           REGISTRATION NO. 333-

                UNITED STATES SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM S-8
                          REGISTRATION STATEMENT UNDER
                           THE SECURITIES ACT OF 1933

                            LAMAR ADVERTISING COMPANY
             (Exact Name of Registrant as Specified in its Charter)


              DELAWARE                                    72-1449411
    (State or Other Jurisdiction                       (I.R.S. Employer
          of Incorporation)                           Identification No.)

               5551 CORPORATE BLVD., BATON ROUGE, LOUISIANA 70808
                    (Address of Principal Executive Offices)

                           1996 EQUITY INCENTIVE PLAN
                            (Full Title of the Plan)

                              KEVIN P. REILLY, JR.
                 Chairman, President and Chief Executive Officer
                            Lamar Advertising Company
                            5551 Corporate Boulevard
                          Baton Rouge, Louisiana 70808
                                 (225) 926-1000
            (Name, Address and Telephone Number of Agent for Service)


                                 with copies to:

                              STANLEY KELLER, ESQ.
                               Palmer & Dodge LLP
                                One Beacon Street
                           Boston, Massachusetts 02108
                                 (617) 573-0100

                         CALCULATION OF REGISTRATION FEE

<TABLE>
<CAPTION>
                                                           PROPOSED MAXIMUM      PROPOSED MAXIMUM
TITLE OF EACH CLASS OF SECURITIES      AMOUNT TO BE       OFFERING PRICE PER    AGGREGATE OFFERING       AMOUNT OF
         TO BE REGISTERED              REGISTERED(1)           SHARE(2)              PRICE(3)        REGISTRATION FEE
---------------------------------      -------------      ------------------   -------------------   ----------------
<S>                                  <C>                 <C>                    <C>                  <C>
Class A Common Stock,
$0.001 par value                      1,000,000 shares         $39.5625             $39,562,500          $10,445
</TABLE>

(1)  Pursuant to Rule 416 under the Securities Act of 1933, to the extent
     additional shares of Lamar Class A common stock may be issued or issuable
     as a result of a stock split or other distribution declared at any time by
     the Board of Directors while this registration statement is in effect, this
     registration statement is hereby deemed to cover all such additional Class
     A common stock.

(2)  Estimated solely for the purpose of determining the registration fee and
     computed pursuant to Rule 457(h) and based upon the average of the high and
     low sale prices on May 24, 2000 as reported by the Nasdaq National Market.

(3)  This Registration Statement registers an additional 1,000,000 shares
     issuable under the registrant's 1996 Equity Incentive Plan (the "Plan").
     The registrant has previously registered 4,000,000 shares issuable under
     the Plan (Registration Statement Nos. 333-10337 and 333-79571).


<PAGE>   2


STATEMENT REGARDING INCORPORATION BY REFERENCE FROM EFFECTIVE REGISTRATION
STATEMENTS.

Pursuant to Instruction E to Form S-8, the registrant incorporates by reference
into this registration statement the contents of the registration statements it
filed on Form S-8 with the SEC on August 16, 1996 (File No. 333-10337) and May
28, 1999 (File No. 333-79571), as amended by Post-Effective Amendment No. 1
thereto filed with the SEC on July 19, 1999, in their entirety, except as to
items set forth below. The Form S-8 filed on August 16, 1996 relates to the
registration of 2,000,000 shares of the registrant's Class A common stock,
$0.001 par value per share authorized for issuance under the registrant's 1996
Equity Incentive Plan (the "Plan"); these 2,000,000 shares of Class A common
stock currently represent 3,000,000 shares of Class A common stock after giving
effect to a 3:2 stock split that became effective on February 27, 1998. The Form
S-8 filed on May 28, 1999 relates to the registration of 1,000,000 shares of the
registrant's Class A common stock authorized for issuance under the Plan. This
Registration Statement provides for the registration of an additional 1,000,000
shares of the registrant's Class A common stock authorized for issuance under
the Plan.

ITEM 8.  EXHIBITS.

         See Exhibit Index on page 5.



<PAGE>   3
                                   SIGNATURES

         Pursuant to the requirements of the Securities Act of 1933, the
registrant certifies that it has reasonable grounds to believe that it meets all
of the requirements for filing on Form S-8 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Baton Rouge, State of Louisiana, on this 25th day of
May, 2000.

                        LAMAR ADVERTISING COMPANY



                        By:  /s/ Kevin P. Reilly, Jr.
                        ---------------------------------------------
                             Kevin P. Reilly, Jr., Chairman, President and Chief
                             Executive Officer

                                POWER OF ATTORNEY

         We, the undersigned officers and directors of Lamar Advertising
Company, hereby severally constitute and appoint Kevin P. Reilly, Jr. and Keith
A. Istre, and each of them singly, our true and lawful attorneys-in-fact, with
full power to them in any and all capacities, to sign any amendments to this
Registration Statement on Form S-8 (including any post-effective amendments
thereto), and to file the same, with exhibits thereto and other documents in
connection therewith, with the Securities and Exchange Commission, hereby
ratifying and confirming all that each of said attorneys-in-fact may do or cause
to be done by virtue hereof.

         Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed below by the following persons in the
capacities indicated on this 25th day of May, 2000:

Signature                                        Capacity
---------                                        --------

/s/ Kevin P. Reilly, Jr.           President, Chief Executive Officer
-------------------------          (Principal Executive Officer) and Director
Kevin P. Reilly, Jr.

/s/ Keith A. Istre                 Chief Financial Officer
-------------------------          (Principal Financial Officer and Principal
Keith A. Istre                     Accounting Officer) and Director

/s/ Charles W. Lamar, III          Director
---------------------------
Charles W. Lamar, III

/s/ Gerald H. Marchand             Director
---------------------------
Gerald H. Marchand

/s/ Stephen P. Mumblow             Director
---------------------------
Stephen P. Mumblow

/s/ Sean E. Reilly                 Director
---------------------------
Sean E. Reilly

/s/ Wendell Reilly                 Director
---------------------------
Wendell Reilly

/s/ T. Everett Stewart, Jr.        Director
---------------------------
T. Everett Stewart, Jr.

                                   Director
---------------------------
Thomas O. Hicks

                                   Director
-------------------------
R. Steven Hicks



<PAGE>   4

                                 EXHIBIT INDEX



       EXHIBIT
       NUMBER         DESCRIPTION
       ------         -----------

       3.1    Certificate of Incorporation of Lamar New Holding Co. Previously
              filed as exhibit 3.1 to the Company's Quarterly Report on Form
              10-Q for the period ended June 30, 1999 (File No. 0-20833) filed
              on August 16, 1999 and incorporated herein by reference.

       3.2    Certificate of Amendment of Certificate of Incorporation of Lamar
              New Holding Co. (whereby the name of Lamar New Holding Co. was
              changed to Lamar Advertising Company). Previously filed as exhibit
              3.2 to the Company's Quarterly Report on Form 10-Q for the period
              ended June 30, 1999 (File No. 0-20833) filed on August 16, 1999
              and incorporated herein by reference.

       3.3    Bylaws of the Company. Previously filed as exhibit 3.3 to the
              Company's Quarterly Report on Form 10-Q for the period ended June
              30, 1999 (File No. 0-20833) filed on August 16, 1999 and
              incorporated herein by reference.

       5      Opinion of Palmer & Dodge LLP as to the legality of the securities
              registered hereunder. Filed herewith.

       23.1   Consent of Palmer & Dodge LLP (contained in Exhibit 5).

       23.2   Consent of KPMG LLP, independent accountants. Filed herewith.

       24     Power of Attorney (included in the signature page hereto).
[{"type": "S-8", "sequence": "1", "description": "FORM S-8", "secsgml_size_bytes": 9224}]
{"company-data": {"conformed-name": "LAMAR ADVERTISING CO/NEW", "cik": "0001090425", "assigned-sic": "7311", "irs-number": "850446801", "state-of-incorporation": "DE", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "S-8", "act": "33", "file-number": "333-37858", "film-number": "643858"}, "business-address": {"street1": "C/O LAMAR ADVERTISING COMPANY", "street2": "5551 CORPORATE BOULEVARD", "city": "BATON ROUGE", "state": "LA", "zip": "70808", "phone": "2259261000"}, "mail-address": {"street1": "C/O LAMAR ADVERTISING COMPANY", "street2": "5551 CORPORATE BOULEVARD", "city": "BATON ROUGE", "state": "LA", "zip": "70808"}, "former-company": {"former-conformed-name": "LAMAR NEW HOLDING CO", "date-changed": "19990716"}}
1
      As filed with the Securities and Exchange Commission on May 25, 2000

                                                           REGISTRATION NO. 333-

                UNITED STATES SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM S-8
                          REGISTRATION STATEMENT UNDER
                           THE SECURITIES ACT OF 1933

                            LAMAR ADVERTISING COMPANY
             (Exact Name of Registrant as Specified in its Charter)

              DELAWARE                                    72-1449411
    (State or Other Jurisdiction                       (I.R.S. Employer
          of Incorporation)                           Identification No.)

               5551 CORPORATE BLVD., BATON ROUGE, LOUISIANA 70808
                    (Address of Principal Executive Offices)

                           1996 EQUITY INCENTIVE PLAN
                            (Full Title of the Plan)

                              KEVIN P. REILLY, JR.
                 Chairman, President and Chief Executive Officer
                            Lamar Advertising Company
                            5551 Corporate Boulevard
                          Baton Rouge, Louisiana 70808
                                 (225) 926-1000
            (Name, Address and Telephone Number of Agent for Service)

                                 with copies to:

                              STANLEY KELLER, ESQ.
                               Palmer & Dodge LLP
                                One Beacon Street
                           Boston, Massachusetts 02108
                                 (617) 573-0100

                         CALCULATION OF REGISTRATION FEE
PROPOSED MAXIMUM      PROPOSED MAXIMUM
TITLE OF EACH CLASS OF SECURITIES      AMOUNT TO BE       OFFERING PRICE PER    AGGREGATE OFFERING       AMOUNT OF
         TO BE REGISTERED              REGISTERED(1)           SHARE(2)              PRICE(3)        REGISTRATION FEE
---------------------------------      -------------      ------------------   -------------------   ----------------
Class A Common Stock,
$0.001 par value                      1,000,000 shares         $39.5625             $39,562,500          $10,445
(1)  Pursuant to Rule 416 under the Securities Act of 1933, to the extent
     additional shares of Lamar Class A common stock may be issued or issuable
     as a result of a stock split or other distribution declared at any time by
     the Board of Directors while this registration statement is in effect, this
     registration statement is hereby deemed to cover all such additional Class
     A common stock.

(2)  Estimated solely for the purpose of determining the registration fee and
     computed pursuant to Rule 457(h) and based upon the average of the high and
     low sale prices on May 24, 2000 as reported by the Nasdaq National Market.

(3)  This Registration Statement registers an additional 1,000,000 shares
     issuable under the registrant's 1996 Equity Incentive Plan (the "Plan").
     The registrant has previously registered 4,000,000 shares issuable under
     the Plan (Registration Statement Nos. 333-10337 and 333-79571).
2

STATEMENT REGARDING INCORPORATION BY REFERENCE FROM EFFECTIVE REGISTRATION
STATEMENTS.

Pursuant to Instruction E to Form S-8, the registrant incorporates by reference
into this registration statement the contents of the registration statements it
filed on Form S-8 with the SEC on August 16, 1996 (File No. 333-10337) and May
28, 1999 (File No. 333-79571), as amended by Post-Effective Amendment No. 1
thereto filed with the SEC on July 19, 1999, in their entirety, except as to
items set forth below. The Form S-8 filed on August 16, 1996 relates to the
registration of 2,000,000 shares of the registrant's Class A common stock,
$0.001 par value per share authorized for issuance under the registrant's 1996
Equity Incentive Plan (the "Plan"); these 2,000,000 shares of Class A common
stock currently represent 3,000,000 shares of Class A common stock after giving
effect to a 3:2 stock split that became effective on February 27, 1998. The Form
S-8 filed on May 28, 1999 relates to the registration of 1,000,000 shares of the
registrant's Class A common stock authorized for issuance under the Plan. This
Registration Statement provides for the registration of an additional 1,000,000
shares of the registrant's Class A common stock authorized for issuance under
the Plan.

ITEM 8.  EXHIBITS.

         See Exhibit Index on page 5.
3
                                   SIGNATURES

         Pursuant to the requirements of the Securities Act of 1933, the
registrant certifies that it has reasonable grounds to believe that it meets all
of the requirements for filing on Form S-8 and has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized, in the City of Baton Rouge, State of Louisiana, on this 25th day of
May, 2000.

                        LAMAR ADVERTISING COMPANY

                        By:  /s/ Kevin P. Reilly, Jr.
                        ---------------------------------------------
                             Kevin P. Reilly, Jr., Chairman, President and Chief
                             Executive Officer

                                POWER OF ATTORNEY

         We, the undersigned officers and directors of Lamar Advertising
Company, hereby severally constitute and appoint Kevin P. Reilly, Jr. and Keith
A. Istre, and each of them singly, our true and lawful attorneys-in-fact, with
full power to them in any and all capacities, to sign any amendments to this
Registration Statement on Form S-8 (including any post-effective amendments
thereto), and to file the same, with exhibits thereto and other documents in
connection therewith, with the Securities and Exchange Commission, hereby
ratifying and confirming all that each of said attorneys-in-fact may do or cause
to be done by virtue hereof.

         Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed below by the following persons in the
capacities indicated on this 25th day of May, 2000:

Signature                                        Capacity
---------                                        --------

/s/ Kevin P. Reilly, Jr.           President, Chief Executive Officer
-------------------------          (Principal Executive Officer) and Director
Kevin P. Reilly, Jr.

/s/ Keith A. Istre                 Chief Financial Officer
-------------------------          (Principal Financial Officer and Principal
Keith A. Istre                     Accounting Officer) and Director

/s/ Charles W. Lamar, III          Director
---------------------------
Charles W. Lamar, III

/s/ Gerald H. Marchand             Director
---------------------------
Gerald H. Marchand

/s/ Stephen P. Mumblow             Director
---------------------------
Stephen P. Mumblow

/s/ Sean E. Reilly                 Director
---------------------------
Sean E. Reilly

/s/ Wendell Reilly                 Director
---------------------------
Wendell Reilly

/s/ T. Everett Stewart, Jr.        Director
---------------------------
T. Everett Stewart, Jr.

                                   Director
---------------------------
Thomas O. Hicks

                                   Director
-------------------------
R. Steven Hicks
4

                                 EXHIBIT INDEX

       EXHIBIT
       NUMBER         DESCRIPTION
       ------         -----------

       3.1    Certificate of Incorporation of Lamar New Holding Co. Previously
              filed as exhibit 3.1 to the Company's Quarterly Report on Form
              10-Q for the period ended June 30, 1999 (File No. 0-20833) filed
              on August 16, 1999 and incorporated herein by reference.

       3.2    Certificate of Amendment of Certificate of Incorporation of Lamar
              New Holding Co. (whereby the name of Lamar New Holding Co. was
              changed to Lamar Advertising Company). Previously filed as exhibit
              3.2 to the Company's Quarterly Report on Form 10-Q for the period
              ended June 30, 1999 (File No. 0-20833) filed on August 16, 1999
              and incorporated herein by reference.

       3.3    Bylaws of the Company. Previously filed as exhibit 3.3 to the
              Company's Quarterly Report on Form 10-Q for the period ended June
              30, 1999 (File No. 0-20833) filed on August 16, 1999 and
              incorporated herein by reference.

       5      Opinion of Palmer & Dodge LLP as to the legality of the securities
              registered hereunder. Filed herewith.

       23.1   Consent of Palmer & Dodge LLP (contained in Exhibit 5).

       23.2   Consent of KPMG LLP, independent accountants. Filed herewith.

       24     Power of Attorney (included in the signature page hereto).