<PAGE>   1
 
     AS FILED WITH THE SECURITIES AND EXCHANGE COMMISSION ON MAY 15, 1998.
 
                                                     REGISTRATION NO.
================================================================================
                    U.S. SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                             ---------------------
 
                                    FORM S-3
            REGISTRATION STATEMENT UNDER THE SECURITIES ACT OF 1933
                             ---------------------
 
                           LAMAR ADVERTISING COMPANY
             (Exact name of registrant as specified in its charter)
 
<TABLE>
<S>                                                 <C>
                     DELAWARE                                           72-1205791
 (State or other jurisdiction of incorporation or         (I.R.S. Employer Identification Number)
                   organization)
</TABLE>
 
                            5551 CORPORATE BOULEVARD
                          BATON ROUGE, LOUISIANA 70808
                                 (504) 926-1000
  (Address, including zip code, and telephone number, including area code, of
                   registrant's principal executive offices)
                             ---------------------
 
                              KEVIN P. REILLY, JR.
                CHAIRMAN, PRESIDENT AND CHIEF EXECUTIVE OFFICER
                           LAMAR ADVERTISING COMPANY
                            5551 CORPORATE BOULEVARD
                          BATON ROUGE, LOUISIANA 70808
                                 (504) 926-1000
 (Name, address, including zip code, and telephone number, including area code,
                             of agent for service)
 
                                with copies to:
 
<TABLE>
<S>                                                 <C>
               STANLEY KELLER, ESQ.                                  R. W. SMITH, JR.
                PALMER & DODGE LLP                                PIPER & MARBURY L.L.P.
                 ONE BEACON STREET                                 CHARLES CENTER SOUTH
            BOSTON, MASSACHUSETTS 02108                           36 SOUTH CHARLES STREET
                  (617) 573-0100                                 BALTIMORE, MARYLAND 21201
                                                                      (410) 539-2530
</TABLE>
 
                             ---------------------
 
        Approximate date of commencement of proposed sale to the public:
 
   FROM TIME TO TIME AFTER THE EFFECTIVE DATE OF THIS REGISTRATION STATEMENT.
                             ---------------------
 
     If the only securities being registered on this form are being offered
pursuant to dividend or interest reinvestment plans, please check the following
box.  [ ]
 
     If any of the securities being registered on this form are to be offered on
a delayed or continuous basis pursuant to Rule 415 under the Securities Act of
1933, other than securities offered only in connection with dividend or interest
reinvestment plans, check the following box.  [X]
 
     If this form is filed to register additional securities for an offering
pursuant to Rule 462(b) under the Securities Act, please check the following box
and list the Securities Act registration statement number of the earlier
effective registration statement for the same offering.  [ ]
 
     If this form is a post-effective amendment filed pursuant to Rule 462(c)
under the Securities Act, check the following box and list the Securities Act
registration statement number of the earlier effective registration statement
for the same offering.  [ ]
 
     If delivery of the prospectus is expected to be made pursuant to Rule 434,
please check the following box.  [ ]
                             ---------------------
 
                        CALCULATION OF REGISTRATION FEE
 
<TABLE>
<CAPTION>
=============================================================================================================================
                                                               PROPOSED MAXIMUM           PROPOSED
  TITLE OF EACH CLASS OF SECURITIES        AMOUNT TO BE       OFFERING PRICE PER     MAXIMUM AGGREGATE         AMOUNT OF
           TO BE REGISTERED                 REGISTERED             SHARE(1)          OFFERING PRICE(1)     REGISTRATION FEE
-----------------------------------------------------------------------------------------------------------------------------
<S>                                    <C>                  <C>                    <C>                    <C>
Class A Common Stock, $0.001 par value
  per share...........................   1,000,000 shares           $33.31              $33,310,000            $9,826.45
=============================================================================================================================
</TABLE>
 
(1) Estimated solely for the purpose of determining the registration fee and
    computed pursuant to Rule 457(c) and based upon the prices on May 14, 1998
    as reported on the consolidated tape for stocks quoted on the Nasdaq
    National Market.
 
     THE REGISTRANT HEREBY AMENDS THIS REGISTRATION STATEMENT ON SUCH DATE OR
DATES AS MAY BE NECESSARY TO DELAY ITS EFFECTIVE DATE UNTIL THE REGISTRANT SHALL
FILE A FURTHER AMENDMENT WHICH SPECIFICALLY STATES THAT THIS REGISTRATION
STATEMENT SHALL THEREAFTER BECOME EFFECTIVE IN ACCORDANCE WITH SECTION 8(a) OF
THE SECURITIES ACT OF 1933 OR UNTIL THE REGISTRATION STATEMENT SHALL BECOME
EFFECTIVE ON SUCH DATE AS THE COMMISSION, ACTING PURSUANT TO SAID SECTION 8(a),
MAY DETERMINE.
================================================================================
<PAGE>   2
 
                   SUBJECT TO COMPLETION, DATED MAY 15, 1998
 
                                1,000,000 SHARES
 
                           LAMAR ADVERTISING COMPANY
 
                              CLASS A COMMON STOCK
                             ---------------------
     This Prospectus relates to the offer and sale of up to 1,000,000 shares
(the "Shares") of Class A Common Stock, $0.001 par value per share ("Class A
Common Stock"), of Lamar Advertising Company (the "Company") by certain existing
stockholders of the Company named herein (the "Selling Stockholders"). The
Company's authorized capital stock includes the shares of Class A Common Stock
and shares of Class B Common Stock, $0.001 par value per share (the "Class B
Common Stock"). The economic rights of the Class A Common Stock and the Class B
Common Stock (collectively, the "Common Stock") are identical, except that each
share of Class A Common Stock entitles the holder thereof to one vote in respect
of matters submitted for the vote of holders of Common Stock, whereas each share
of Class B Common Stock entitles the holder thereof to ten votes on such
matters. The Reilly Family Limited Partnership (the "RFLP"), one of the Selling
Stockholders, owns all of the outstanding shares of Class B Common Stock and
will be selling shares of such Class B Common Stock, which will convert
automatically, on a one-for-one basis, into shares of Class A Common Stock upon
such sale. The Shares may be offered and sold by the Selling Stockholders from
time to time directly to Purchasers, through agents, through dealers, through
underwriters or through a combination of any such methods of sale. The Shares
may be sold in one or more transactions at a fixed price or a price which may be
changed, at market prices prevailing at the time of sale, at prices relating to
prevailing market prices or at a negotiated price. The Company will not receive
any of the proceeds from the sale of the Shares. See "Selling Stockholders" and
"Plan of Distribution."
 
     The Class A Common Stock is quoted on The Nasdaq National Market under the
symbol "LAMR." On May 14, 1998, the last reported per share sale price of Class
A Common Stock was $33.25.
 
     SEE "RISK FACTORS" BEGINNING ON PAGE 2 OF THIS PROSPECTUS FOR A DISCUSSION
OF CERTAIN FACTORS THAT SHOULD BE CONSIDERED BY PROSPECTIVE PURCHASERS OF THE
SHARES OF CLASS A COMMON STOCK OFFERED HEREBY.
 
                             ---------------------
 
  THESE SECURITIES HAVE NOT BEEN APPROVED OR DISAPPROVED BY THE SECURITIES AND
 EXCHANGE COMMISSION OR ANY STATE SECURITIES COMMISSION NOR HAS THE SECURITIES
   AND EXCHANGE COMMISSION OR ANY STATE SECURITIES COMMISSION PASSED UPON THE
ACCURACY OR ADEQUACY OF THIS PROSPECTUS. ANY REPRESENTATION TO THE CONTRARY IS A
                               CRIMINAL OFFENSE.
 
                             ---------------------
 
     NO PERSON IS AUTHORIZED TO GIVE ANY INFORMATION OR TO MAKE ANY
REPRESENTATIONS OTHER THAN THOSE CONTAINED IN THIS PROSPECTUS AND, IF GIVEN OR
MADE, SUCH INFORMATION OR REPRESENTATIONS MUST NOT BE RELIED UPON AS HAVING BEEN
AUTHORIZED BY THE COMPANY OR THE SELLING STOCKHOLDERS. THIS PROSPECTUS DOES NOT
CONSTITUTE AN OFFER TO SELL OR A SOLICITATION OF AN OFFER TO BUY TO ANY PERSON
IN ANY JURISDICTION IN WHICH SUCH OFFER OR SOLICITATION WOULD BE UNLAWFUL OR TO
ANY PERSON TO WHOM IT IS UNLAWFUL. NEITHER THE DELIVERY OF THIS PROSPECTUS NOR
ANY OFFER OR SALE MADE HEREUNDER SHALL, IN ANY CIRCUMSTANCES, CREATE ANY
IMPLICATION THAT THERE HAS BEEN NO CHANGE IN THE AFFAIRS OF THE COMPANY OR THAT
THE INFORMATION CONTAINED HEREIN IS CORRECT AS OF ANY TIME SUBSEQUENT TO THE
DATE HEREOF.
 
                             ---------------------
 
                  The date of this Prospectus is May   , 1998.
<PAGE>   3
 
                                  THE COMPANY
 
     Lamar Advertising Company is one of the largest and most experienced owners
and operators of outdoor advertising structures in the United States. It
conducts a business that has operated under the Lamar name since 1902. A more
complete description of the business of the Company and its recent activities
can be found in the documents listed in "Incorporation of Certain Documents by
Reference." The principal offices of the Company, a Delaware corporation, are
located at 5551 Corporate Boulevard, Baton Rouge, Louisiana 70808, and its
telephone number at such offices is (504) 926-1000.
 
                             AVAILABLE INFORMATION
 
     The Company is subject to the informational requirements of the Securities
Exchange Act of 1934, as amended (the "Exchange Act"), and in accordance
therewith, files periodic reports, proxy statements and other information with
the Securities and Exchange Commission (the "Commission") relating to its
business, financial statements and other matters. Reports and proxy and
information statements filed with the Commission as well as copies of the
Registration Statement of which this Prospectus is a part can be inspected and
copied at the public reference facilities maintained by the Commission at Room
1024, 450 Fifth Street, N.W., Judiciary Plaza, Washington, D.C. 20549, and at
the following Regional Offices of the Commission: Midwest Regional Office, 500
West Madison Avenue, Suite 1400, Chicago, Illinois 60661; and Northeast Regional
Office, Seven World Trade Center, Suite 1300, New York, New York 10048. Copies
of such material can also be obtained at prescribed rates from the public
reference section of the Commission at its principal office at 450 Fifth Street,
N.W., Judiciary Plaza, Washington, D.C. 20549. Such reports and other
information can also be reviewed on the Commission's web site
(http://www.sec.gov).
 
                INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE
 
     The Company hereby incorporates in this Prospectus by reference the
following documents heretofore filed with the Commission (File No. 1-12407)
pursuant to the Exchange Act: (i) the Company's Annual Report on Form 10-K for
the year ended December 31, 1997; (ii) the Company's Quarterly Report on Form
10-Q for the quarter ended March 31, 1998; (iii) the Company's Current Report on
Form 8-K/A filed with the Commission on April 17, 1998; and (iv) the description
of the Class A Common Stock contained in the Company's Registration Statement on
Form 8-A filed with the Commission on June 7, 1996, as amended by Form 8-A/A
filed with the Commission on July 31, 1996.
 
     All documents filed by the Company pursuant to Sections 13(a), 13(c), 14 or
15(d) of the Exchange Act subsequent to the date of this Prospectus and prior to
termination of the offering made hereby shall be deemed to be incorporated in
this Prospectus by reference and to be a part hereof from the respective dates
of the filing of such documents. Any statement contained herein or in a document
incorporated or deemed to be incorporated by reference herein shall be deemed to
be modified or superseded for purposes of this Prospectus to the extent that a
statement contained herein or in any subsequently filed document which also is,
or is deemed to be, incorporated by reference herein, modifies or supersedes
such statement. Any statement so modified or superseded shall not be deemed,
except as so modified or superseded, to constitute part of this Prospectus.
 
     The Company hereby undertakes to provide without charge to each person to
whom a copy of this Prospectus has been delivered, upon the written or oral
request of any such person, a copy of any and all of the documents referred to
above which have been or may be incorporated in this Prospectus by reference,
other than exhibits to such documents which are not specifically incorporated by
reference into such documents. Requests for such copies should be directed to
the executive offices of Lamar Advertising Company, 5551 Corporate Boulevard,
Baton Rouge, Louisiana 70808, Attention: Investor Relations, telephone (504)
926-1000.
<PAGE>   4
 
                                  RISK FACTORS
 
     In addition to the other information contained and incorporated by
reference in this Prospectus, the following factors should be considered
carefully in evaluating an investment in the Shares offered hereby.
 
     This Prospectus, including documents incorporated by reference, contains
"forward-looking statements" within the meaning of Section 27A of the Securities
Act of 1933, as amended (the "Securities Act"), and Section 21E of the
Securities Exchange Act of 1934, as amended (the "Exchange Act"). Such forward-
looking statements involve risks and uncertainties that could cause the actual
results, performance or achievements of the Company, or industry results, to
differ materially from the results, performance or achievements expressed or
implied by such forward-looking statements. Such risks and uncertainties
include, among others, the risks and uncertainties described under the caption
"Risk Factors" in this Prospectus. These forward-looking statements speak only
as of the date of this Prospectus. The Company expressly disclaims any
obligation or undertaking to disseminate any updates or revisions to any
forward-looking statement contained herein to reflect any change in the
Company's expectations with regard thereto or any change in events, conditions
or circumstances on which any such statement is based.
 
SUBSTANTIAL INDEBTEDNESS OF THE COMPANY
 
     The Company presently has substantial indebtedness and may incur additional
indebtedness in the future. As of December 31, 1997 the Company's indebtedness
was approximately $541.5 million and the Company had approximately $165.0
million available for borrowing under the Company's credit facility (the "Senior
Credit Facility") with a syndicate of commercial banks (excluding the $75
million available under the facility funded at the discretion of the lenders).
Additionally, as of December 31, 1997, the Company had $3.6 million of Class A
Preferred Stock, $638 par value per share, outstanding which is entitled to a
cumulative preferential dividend of $364,903 annually. A substantial part of the
Company's cash flow from operations is dedicated to debt service and is not
available for other purposes. Further, if the Company's net cash provided by
operating activities were to decrease from present levels, the Company could
experience difficulty in meeting its debt service obligations without additional
financing. There can be no assurance that, in the event the Company were to
require additional financing, such additional financing would be available or,
if available, would be available on favorable terms. In addition, any such
additional financing may require the consent of lenders under the Senior Credit
Facility or holders of other debt of the Company. Certain of the Company's
competitors operate on a less leveraged basis and may have greater operating and
financial flexibility than the Company.
 
RESTRICTIVE COVENANTS IN DEBT INSTRUMENTS
 
     The Senior Credit Facility and the Company's indentures relating to the
Company's $255 million outstanding 9 5/8% Senior Subordinated Notes due 2006 and
$200 million outstanding 8 5/8% Senior Subordinated Notes due 2007 (the
"Existing Indentures") contain covenants that restrict, among other things, the
ability of the Company to dispose of assets, incur or repay debt, create liens,
and make certain investments. In addition, the Senior Credit Facility requires
the Company to maintain specified financial ratios and levels including cash
interest coverage, fixed charge coverage, senior debt and total debt ratios. The
ability of the Company to comply with the foregoing restrictive covenants, and
any restrictive covenants contained in future agreements, will depend on its
future performance, which is subject to prevailing economic, financial and
business conditions and other factors beyond the Company's control.
 
FLUCTUATIONS IN ECONOMIC AND ADVERTISING TRENDS
 
     The Company relies on sales of advertising space for its revenues, and its
operating results are therefore affected by general economic conditions, as well
as trends in the advertising industry. A reduction in advertising expenditures
available for the Company's displays could result from a general decline in
economic conditions, a decline in economic conditions in particular markets
where the Company conducts business or a reallocation of advertising
expenditures to other available media by significant users of the Company's
displays. Although the Company believes that in recent years outdoor advertising
expenditures have increased
 
                                        2
<PAGE>   5
 
more rapidly than total U.S. advertising expenditures, there can be no assurance
that this trend will continue or that in the future outdoor advertising
expenditures will not grow more slowly than the advertising industry as a whole.
 
POTENTIAL ELIMINATION OR REDUCTION OF TOBACCO ADVERTISING
 
     Approximately 9% of the Company's outdoor advertising net revenues and 8%
of consolidated net revenues in fiscal 1997 came from the tobacco products
industry, compared to 10% of outdoor advertising net revenues for fiscal 1996,
9% for fiscal 1995, 7% for fiscal 1994 and 1993, and 12% for fiscal 1992. The
tobacco percentage for the three months ended March 31, 1998 was approximately
9%. Manufacturers of tobacco products, principally cigarettes, were historically
major users of outdoor advertising displays. Beginning in 1992, the leading
tobacco companies substantially reduced their domestic advertising expenditures
in response to societal and governmental pressures and other factors. There can
be no assurance that the tobacco industry will not further reduce advertising
expenditures in the future either voluntarily or as a result of governmental
regulation or as to what affect any such reduction may have on the Company.
 
     In June 1997 several of the major tobacco companies in the United States
and numerous state attorneys general reached agreement on a proposed settlement
of litigation between such parties. The terms of this proposed settlement
include a ban on all outdoor advertising of tobacco products commencing nine
months after finalization of the settlement. The settlement, however, is subject
to numerous conditions, the most notable of which is the enactment of
legislation by the federal government. Such legislation is still pending before
Congress. At this time, it is uncertain when a definitive settlement will be
reached, if at all, or what the terms of any such settlement will be. An
elimination or reduction in billboard advertising by the tobacco industry could
cause an immediate reduction in the Company's outdoor advertising revenues and
may simultaneously increase the Company's available inventory. An increase in
available inventory could result in the Company reducing its rates or limiting
its ability to raise rates for some period of time. If the tobacco litigation
settlement were to be finalized in its current form and if the Company were
unable to replace revenues from tobacco advertising with revenues from other
sources, such settlement could have a material adverse effect on the Company's
results of operations. While the Company believes that it would be able to
replace a substantial portion of revenues from tobacco advertising that would be
eliminated due to such a settlement with revenues from other sources, any
replacement of tobacco advertising may take time and require a reduction in
advertising rates.
 
     In addition, the states of Florida, Mississippi, Texas and Minnesota have
entered into separate settlements of litigation with the tobacco industry. None
of these settlements is conditioned on federal government approval. The Florida
and Mississippi settlements provided for the elimination of all outdoor
advertising of tobacco products by February 1998 in such states and at such time
all of the Company's tobacco billboards and advertising was removed. The Texas
settlement requires the elimination of all outdoor advertising of tobacco
products by June 1998 and the Minnesota settlement requires the elimination of
all outdoor advertising of tobacco products by November 1998. The Company
operates approximately 4,253 outdoor advertising displays in seven markets in
Florida and approximately $1.8 million of its approximately $19.2 million in net
revenues in Florida during 1997 were attributable to tobacco advertising. The
Company operates approximately 2,532 outdoor advertising displays in three
markets in Mississippi and approximately $0.8 million of its approximately $10.6
million in net revenues in Mississippi during 1997 were attributable to tobacco
advertising. The Company operates approximately 3,300 outdoor advertising
displays in six markets in Texas and approximately $0.8 million of its
approximate $11.0 million in net revenues in Texas during 1997 and approximately
$0.3 million of its approximate $3.2 million in net revenues in Texas for the
three months ended March 31, 1998 were attributable to tobacco advertising.
Although the Company does not operate any outdoor advertising displays for
tobacco products in Minnesota, the size and scope of the Minnesota settlement,
including the ban on tobacco outdoor advertising, may foreshadow similar
settlements of tobacco-related claims and litigation which may also adversely
affect outdoor advertising revenues.
 
                                        3
<PAGE>   6
 
REGULATION OF OUTDOOR ADVERTISING
 
     The outdoor advertising business is subject to regulation by federal, state
and local governments. Federal law requires states, as a condition to federal
highway assistance, to restrict billboards on federally-aided primary and
interstate highways to commercial and industrial areas and imposes certain
additional size, spacing and other limitations on billboards. Some states have
adopted standards more restrictive than the federal requirements. Local
governments generally control billboards as part of their zoning regulations,
and some local governments prohibit construction of new billboards and
reconstruction of substantially damaged billboards or allow new construction
only to replace existing structures. In addition, some jurisdictions (including
certain of those within the Company's markets) have adopted amortization
ordinances under which owners and operators of outdoor advertising displays are
required to remove existing structures at some future date, often without
condemnation proceeds being available. Federal and corresponding state outdoor
advertising statutes require payment of compensation for removal by governmental
order in some circumstances. Ordinances requiring the removal of a billboard
without compensation, whether through amortization or otherwise, have been
challenged in various state and federal courts on both statutory and
constitutional grounds, with conflicting results. Although the Company has been
successful in the past in negotiating acceptable arrangements in circumstances
in which its displays have been subject to removal or amortization, there can be
no assurance that the Company will be successful in the future and what effect,
if any, such regulations may have on the Company's operations. In addition, the
Company is unable to predict what additional regulation may be imposed on
outdoor advertising in the future. Legislation regulating the content of
billboard advertisements has been introduced in Congress from time to time in
the past, although no laws which, in the opinion of management, would materially
and adversely affect the Company's business have been enacted to date. Changes
in laws and regulations affecting outdoor advertising at any level of government
may have a material adverse effect on the Company's results of operations. See
"-- Potential Elimination or Reduction of Tobacco Advertising" for a discussion
of recent developments concerning tobacco advertising.
 
ACQUISITION AND GROWTH STRATEGY RISKS
 
     The Company's growth has been enhanced materially by strategic acquisitions
that have substantially increased the Company's inventory of advertising
displays. One element of the Company's operating strategy is to make strategic
acquisitions in markets in which it currently competes as well as in new
markets. While the Company believes that the outdoor advertising industry is
highly fragmented and that significant acquisition opportunities are available,
the market has been consolidating and there can be no assurance that suitable
acquisition candidates can continue to be found. In addition, the Company is
likely to face increased competition from other outdoor advertising companies
for available acquisition opportunities. Also, if the prices sought by sellers
of outdoor advertising displays continue to rise, as management believes may
happen, the Company may find fewer acceptable acquisition opportunities. There
can be no assurance that the Company will have sufficient capital resources to
complete acquisitions or be able to obtain any required consents of its bank
lenders or that acquisitions can be completed on terms acceptable to the
Company.
 
     During 1997, the Company completed the acquisition of 24 complementary
businesses. The process of integrating these businesses into the Company's
operations may result in unforeseen operating difficulties and could require
significant management attention that would otherwise be available for the
development of the Company's existing business. Moreover, there can be no
assurance that the Company will realize anticipated benefits and cost savings or
that any future acquisitions will be consummated.
 
COMPETITION
 
     In addition to competition from other forms of media, including television,
radio, newspapers and direct mail advertising, the Company faces competition in
its markets from other outdoor advertising companies, some of which may be
larger and better capitalized than the Company. The Company also competes with a
wide variety of other out-of-home advertising media, the range and diversity of
which have increased substantially over the past several years to include
advertising displays in shopping centers, malls, airports, stadiums, movie
theaters and supermarkets, and on taxis, trains and buses. The Company believes
that its local orientation, including the maintenance of local offices, has
enabled it to compete successfully in its
                                        4
<PAGE>   7
 
markets to date. However, there can be no assurance that the Company will be
able to continue to compete successfully against current and future sources of
outdoor advertising competition and competition from other media or that the
competitive pressures faced by the Company will not adversely affect its
profitability or financial performance. In its logo sign business, the Company
currently faces competition for state franchises from two other logo sign
providers as well as local companies. Competition from these sources is
encountered both when a franchise is first privatized and upon renewal
thereafter.
 
POTENTIAL LOSSES FROM HURRICANES
 
     A significant portion of the Company's structures are located in the
mid-Atlantic and Gulf Coast regions of the United States. These areas are highly
susceptible to hurricanes during the late summer and early fall. In the past,
severe storms have caused the Company to incur material losses resulting from
structural damage, overtime compensation, loss of billboards that could not
legally be replaced and reduced occupancy because billboards are out of service.
The Company has determined that it is not economical to obtain insurance against
losses from hurricanes and other storms. The Company has developed contingency
plans to deal with the threat of hurricanes, including plans for early removal
of advertising faces to permit the structures to better withstand high winds and
the replacement of such faces after storms have passed. As a result of these
contingency plans, the Company has experienced lower levels of losses from
recent storms and hurricanes. Structural damage attributable to Hurricane Andrew
in 1992 was less than $500,000, and the Company suffered no significant
structural damage due to hurricanes in 1996 or 1997. There can be no assurance
that the Company's contingency plans will be effective.
 
RISKS IN OBTAINING AND RETAINING LOGO SIGN FRANCHISES
 
     Logo sign franchises represent a growing portion of the Company's revenues
and operating income. The Company cannot predict the number of remaining states,
if any, that will initiate logo sign programs or convert state-run logo sign
programs to privately operated programs. Competition for new state logo sign
franchises is intense and, even after a favorable award, franchises may be
subject to challenge under state contract bidding requirements, resulting in
delays and litigation costs. In addition, state logo sign franchises are
generally, with renewal options, ten to twenty-year franchises subject to
earlier termination by the state, in most cases upon payment of compensation.
Typically, at the end of the term of the franchise, ownership of the structures
is transferred to the state without compensation to the Company. Although none
of the Company's logo sign franchises is due to terminate in the next two years,
three are subject to renewal during that period. There can be no assurance that
the Company will be successful in obtaining new logo sign franchises or renewing
existing franchises. Furthermore, following the receipt by the Company of a new
state logo sign franchise, the Company generally incurs significant start-up
capital expenditures and there can be no assurance that the Company will
continue to have access to capital to fund such expenditures.
 
RELIANCE ON KEY EXECUTIVES
 
     The Company's success depends to a significant extent upon the continued
services of its executive officers and other key management and sales personnel,
in particular Kevin P. Reilly, Jr., the Company's Chief Executive Officer, the
Company's six regional managers and the manager of its logo sign business.
Although the Company believes it has incentive and compensation programs
designed to retain key employees, the Company has no employment contracts with
any of its employees, and none of its executive officers are bound by
non-compete agreements. The Company does not maintain key man insurance on its
executives. The unavailability of the continuing services of any of its
executive officers and other key management and sales personnel could have an
adverse effect on the Company's business.
 
CONTROLLING STOCKHOLDER
 
     The Reilly Family Limited Partnership (the "RFLP"), of which Kevin P.
Reilly, Jr., the Company's Chief Executive Officer, is the managing general
partner, on the date of this Prospectus beneficially owns shares of the
Company's common stock (the "Common Stock") having approximately 86.7% of the
total voting power of the Common Stock. As a result, Mr. Reilly, or his
successor as managing general partner, will
                                        5
<PAGE>   8
 
effectively be able to control the outcome of matters requiring a stockholder
vote, including electing directors, adopting or amending certain provision's of
the Company's certificate of incorporation and by-laws and approving or
preventing certain mergers or other similar transactions, such as a sale of
substantially all the Company's assets (including transactions that could give
holders of the Company's Class A Stock the opportunity to realize a premium over
the then-prevailing market price for their shares). In addition, the Company's
officers, directors and their respective affiliates other than the RFLP, on the
date of this Prospectus beneficially own shares of the Company's Common Stock
having approximately 2.5% of the total voting power of the Company's Common
Stock. Therefore, purchasers of the Class A Stock offered hereby will become
minority stockholders of the Company and will be unable to control the
management or business policies of the Company. Moreover, subject to contractual
restrictions and general fiduciary obligations, the Company is not prohibited
from engaging in transactions with its management and principal stockholders, or
with entities in which such persons are interested. The Company's certificate of
incorporation does not provide for cumulative voting in the election of
directors and, as a result, the controlling stockholders can elect all the
directors if they so choose.
 
CERTAIN ANTI-TAKEOVER PROVISIONS
 
     Certain provisions of the Company's certificate of incorporation and
by-laws may have the effect of discouraging a third party from making an
acquisition proposal for the Company and thereby inhibiting a change in control
of the Company in circumstances that could give the holders of the Class A Stock
the opportunity to realize a premium over the then-prevailing market price of
such stock. Such provisions may also adversely affect the market price of the
Class A Stock. For example, the Company's certificate of incorporation
authorizes the issuance of "blank check" Preferred Stock with such designations,
rights and preferences as may be determined from time to time by the Board of
Directors. In the event of issuance, such Preferred Stock could be utilized,
under certain circumstances, as a method of discouraging, delaying or preventing
a change in control of the company. In addition, the issuance of Preferred Stock
may adversely affect the voting and dividend rights, rights upon liquidation and
other rights of the holders of Class A Stock. Although the company has no
present intention to issue any shares of such Preferred Stock, the Company
retains the right to do so in the future. Furthermore, the Company is subject to
Section 203 of the Delaware General Corporation Law. The existence of this
provision, as well as the control of the Company by the RFLP, would be expected
to have an anti-takeover effect, including possibly discouraging takeover
attempts that might result in a premium over the market price for the shares of
Class A Stock.
 
VOLATILITY OF STOCK PRICE
 
     From time to time, there may be significant volatility in the market price
for the Class A Stock. Quarterly operating results of the Company, changes in
earnings estimates by analysts, changes in general conditions in the Company's
industry or the economy or the financial markets or other developments affecting
the Company could cause the market price of the Class A Stock to fluctuate
substantially. Fluctuations may also occur as a result of some degree of
seasonality in the Company's earnings and operating results. Typically, the
Company experiences its strongest financial performance in the summer and its
lowest in the winter. The Company expects this trend to continue in the future.
Because a significant portion of the Company's expenses are fixed, a reduction
in revenues in any quarter is likely to result in a period to period decline in
operating performance and net earnings. In addition, in recent years the stock
market has experienced significant price and volume fluctuations. This
volatility has had a significant effect on the market price of securities issued
by many companies for reasons unrelated to their operating performance.
 
                                        6
<PAGE>   9
 
                                USE OF PROCEEDS
 
     The Company will not receive any proceeds from the sale of the Shares.
 
                              SELLING STOCKHOLDERS
 
     All of the Shares offered hereby are being offered by the Selling
Stockholders. The following table sets forth the name of each Selling
Stockholder and the number of Shares owned by each such holder:
 
<TABLE>
<CAPTION>
                                    BENEFICIAL OWNERSHIP                    BENEFICIAL OWNERSHIP
                                      PRIOR TO OFFERING                       AFTER OFFERING(7)
                                  -------------------------               -------------------------
                                                PERCENT OF     SHARES                   PERCENT OF
                                    NUMBER      OUTSTANDING     BEING       NUMBER      OUTSTANDING
                                  OF SHARES       SHARES       OFFERED    OF SHARES       SHARES
                                  ----------    -----------    -------    ----------    -----------
<S>                               <C>           <C>            <C>        <C>           <C>
Reilly Family Limited
  Partnership(1)................  18,762,912       39.5%       675,000    18,087,912       38.1%
Charles W. Lamar, III...........   5,250,665(2)    18.3%       125,000     5,125,665       17.9%
Mary Lee Lamar Dixon............   2,487,727(3)     8.7%        75,000     2,412,727        8.4%
Allison J. Lamar................     720,778(4)     2.5%        25,000       695,778        2.4%
Courtney J. Lamar...............     777,796(5)     2.7%        50,000       727,796        2.5%
Madison C. Lamar................     777,796(6)     2.7%        50,000       727,796        2.5%
</TABLE>
 
---------------
 
(1) Amounts shown under "Number of Shares" and "Percentage of Outstanding
    Shares" for the Reilly Family Limited Partnership include shares of Class B
    Common Stock held by the Reilly Family Limited Partnership and assume the
    conversion of all Shares of Class B Common Stock into Class A Common Stock.
    Upon the sale of any shares of Class B Common Stock to individuals and
    entities other than a limited number of members of the Reilly family, such
    shares automatically convert into shares of Class A Common Stock.
 
(2) Includes 1,555,592 shares held in trust for Mr. Lamar's two minor children,
    as to which Mr. Lamar disclaims beneficial ownership, and 1,500,000 shares
    held by CWL3, LLC, as to which Mr. Lamar is the beneficial owner.
 
(3) Includes 817,821 shares of Class A Stock held in a trust, of which LaBanc &
    Co. is the nominee of the trustee, for the benefit of Mrs. Dixon, as to
    which Mrs. Dixon disclaims beneficial ownership, and 1,650,000 shares held
    by Mary Lee Lamar Dixon Family LLC (75,000 of which are being offered
    hereby), as to which Mrs. Dixon is the beneficial owner.
 
(4) Includes 321,459 shares held in a trust (25,000 of which are being offered
    hereby) as to which Ms. Lamar is the beneficial owner. Charles W. Lamar, III
    disclaims beneficial ownership of such shares.
 
(5) Consists of shares held in a trust as to which Ms. Lamar is the beneficial
    owner. Charles W. Lamar, III disclaims beneficial ownership of such shares.
 
(6) Consists of shares held in a trust as to which Mr. Lamar is the beneficial
    owner. Charles W. Lamar, III disclaims beneficial ownership of such shares.
 
(7) Assumes all shares offered are sold, and no purchases or sales by the
    Company are made between the date of this Prospectus and the completion of
    such sales.
 
     Kevin P. Reilly, Jr., the Chairman, President and Chief Executive Officer
of the Company, is the managing general partner of the RFLP and Mr. Reilly's
three siblings, Anna Reilly Cullinan, Sean E. Reilly and Wendell S. Reilly are
the other general partners of the RFLP. Sean Reilly is the Company's Director of
Mergers & Acquisitions and Real Estate. Mr. Reilly and Charles W. Lamar, III are
cousins.
 
     As managing general partner, Kevin Reilly has the ability to vote all
shares of the Company's stock owned by the RFLP and, with the approval of the
partners owning a majority of the general partner interests, to dispose of such
shares. Kevin Reilly and his three siblings each hold equal general partner
interests. If all of the Shares are sold, the RFLP will have approximately 86.4%
of the total voting power of the Common Stock.
 
     Charles W. Lamar, III is General Counsel, Secretary, and a director of the
Company. Mary Lee Lamar Dixon is Mr. Lamar's sister. Allison Lamar and Courtney
Lamar are Mr. Lamar's daughters, and Madison Lamar is Mr. Lamar's son.
 
                                        7
<PAGE>   10
 
                              PLAN OF DISTRIBUTION
 
     The Shares offered hereby may be sold from time to time at prices then
prevailing, prices related to the then-current market price, negotiated prices
or fixed prices. Such sales may be made through underwriters, dealers or agents
or directly to purchasers.
 
     The Selling Shareholders may effect sales through brokers who may receive
compensation in the form of commissions or discounts from the Selling
Stockholders, the purchasers of the Shares or both (which compensation to a
particular broker might be in excess of customary commissions). Such brokers may
be deemed to be "underwriters" within the meaning of the Securities Act, in
connection with such sales, and any commissions or discounts received by them
may be deemed to constitute underwriting discounts or commissions.
 
     Upon the Company being notified by a Selling Stockholder that any material
arrangement has been entered into with a broker for the sale of Shares, if
required, a prospectus supplement disclosing facts material to the transaction
will accompany this Prospectus. If underwriters are used in a sale, for example,
this Prospectus will be accompanied by a supplement naming such underwriters and
setting forth any initial public offering price, any underwriting discounts or
commissions and any concessions allowed or reallowed to dealers.
 
     In an underwritten offering, the underwriters will acquire Shares for their
own accounts and may resell the Shares from time to time in one or more
transactions, including negotiated transactions, at a fixed public offering
price or at varying prices determined at the time of sale. The Shares may be
offered to the public either through underwriting syndicates represented by one
or more managing underwriters or directly by one or more firms acting as
underwriters.
 
     Underwriters, dealers, agents and other persons may be entitled, under
agreements entered into with the Company, to indemnification by the Company
against certain civil liabilities, including liabilities under the Securities
Act, or to contribution with respect to payments which they may be required to
make in respect thereof. Underwriters and agents may engage in transaction with,
or perform services for, the Company in the ordinary course of business.
 
     The Company has agreed to bear all normal and reasonable costs (other
brokerage discounts or commissions) in connection with the registration of the
Shares under the Securities Act for sale by the Selling Stockholders and
quotation of the Shares on the Nasdaq National Market. The Company has also
agreed to indemnify the Selling Stockholders against certain civil liabilities,
including liabilities under the Securities Act.
 
                                 LEGAL MATTERS
 
     The validity of the Shares will be passed upon for the Company by Palmer &
Dodge LLP, Boston, Massachusetts.
 
                                    EXPERTS
 
     The consolidated financial statements and schedule of Lamar Advertising
Company and Subsidiaries as of October 31, 1996 and December 31, 1997, and for
the years ended October 31, 1995 and 1996, the two months ended December 31,
1996, and the year ended December 31, 1997, incorporated by reference into this
Prospectus and Registration Statement have been incorporated by reference herein
and in the Registration Statement in reliance upon the report of KPMG Peat
Marwick LLP, independent certified public accountants, incorporated by reference
herein, and upon the authority of such firm as experts in accounting and
auditing.
 
     The consolidated balance sheets of Penn Advertising, Inc. and subsidiaries
as of December 31, 1996 and 1995 and the related consolidated statements of
income and accumulated deficit and cash flows for the years then ended have been
incorporated by reference herein and in the Registration Statement in reliance
upon the
 
                                        8
<PAGE>   11
 
report of Philip R. Friedman and Associates, independent certified public
accountants, incorporated by reference herein and upon the authority of said
firm as experts in accounting and auditing.
 
     The statement of assets acquired and liabilities assumed of National
Advertising Company -- Lamar Acquisition as of August 14, 1997, and the related
statement of revenues and expenses for the years ended December 31, 1996 and
1995, incorporated by reference in this prospectus, have been incorporated
herein in reliance on the report of Coopers & Lybrand L.L.P., independent
accountants, given on the authority of that firm as experts in accounting and
auditing.
 
                                        9
<PAGE>   12
 
                                    PART II
 
                     INFORMATION NOT REQUIRED IN PROSPECTUS
 
ITEM 14. OTHER EXPENSES OF ISSUANCE AND DISTRIBUTION
 
     Expenses in connection with the offering of the Shares will be borne by the
Selling Stockholders and are estimated as follows:
 
<TABLE>
<S>                                                <C>
SEC Registration Fee.............................  $ 9,956.00
Legal fees and expenses..........................  $ 7,500.00
Miscellaneous expenses...........................  $ 2,544.00
                                                   ----------
  Total..........................................  $20,000.00
                                                   ==========
</TABLE>
 
ITEM 15. INDEMNIFICATION OF DIRECTORS AND OFFICERS
 
     Section 145 of the Delaware General Corporation Law grants the registrant
the power to indemnify each person who was or is a party or is threatened to be
made a party to any threatened, pending or completed action, suit or proceeding,
whether civil, criminal, administrative or investigative by reason of the fact
that he is or was a director, officer, employee or agent of the registrant, or
is or was serving at the request of the registrant as a director, officer,
employee or agent of another corporation, partnership, joint venture, trust or
other enterprise, against expenses (including attorneys' fees), judgments, fines
and amounts paid in settlement actually and reasonably incurred by him in
connection with any such action, suit or proceeding if he acted in good faith
and in a manner he reasonably believed to be in or not opposed to the best
interests of the registrant, and with respect to any criminal action or
proceeding, had no reasonable cause to believe his conduct was unlawful,
provided, however, no indemnification shall be made in connection with any
proceeding brought by or in the right of the registrant where the person
involved is adjudged to be liable to the registrant except to the extent
approved by a court.
 
     The registrant's By-laws provide that any person who is made a party to any
action or proceeding because such person is or was a director or officer of the
registrant will be indemnified and held harmless against all claims, liabilities
and expenses, including those expenses incurred in defending a claim and amounts
paid or agreed to be paid in connection with reasonable settlements made before
final adjudication with the approval of the Board of Directors, if such person
has not acted, or in the judgement or the shareholders or directors of the
registrant has not acted, with willful or intentional misconduct. The
indemnification provided for in the registrant's By-laws is expressly not
exclusive of any other rights to which those seeking indemnification may be
entitled as a matter of law.
 
     The registrant's Certificate of Incorporation (the "Certificate") provides
that directors of the registrant will not be personally liable to the Company or
its stockholders for monetary damages for breach of fiduciary duty as a
director, whether or not an individual continues to be a director at the time
such liability is asserted, except for liability (i) for any breach of the
director's duty of loyalty to the registrant or its stockholders, (ii) for acts
or omissions not in good faith or which involve intentional misconduct or a
knowing violation of law, (iii) under Section 174 of the DGCL, relating to
prohibited dividends or distributions or the repurchase or redemption of stock,
or (iv) for any transaction from which the director derives an improper personal
benefit.
 
ITEM 16. EXHIBITS
 
     See Exhibit Index immediately following the signature page hereof.
 
                                      II-1
<PAGE>   13
 
ITEM 17. UNDERTAKINGS
 
     (a) The undersigned registrant hereby undertakes:
 
          (1) To file, during any period in which offers or sales are being
     made, a post-effective amendment to this registration statement:
 
             (i) To include any prospectus required by Section 10(a)(3) of the
        Securities Act of 1933;
 
             (ii) To reflect in the prospectus any facts or events arising after
        the effective date of the registration statement (or the most recent
        post-effective amendment thereof) which, individually or in the
        aggregate, represent a fundamental change in the information set forth
        in the registration statement. Notwithstanding the foregoing, any
        increase or decrease in volume of securities offered (if the total
        dollar value of securities offered would not exceed that which was
        registered) and any deviation from the low or high and of the estimated
        maximum offering range may be reflected in the form of prospectus filed
        with the Commission pursuant to Rule 424(b) if, in the aggregate, the
        changes in volume and price represent no more than 20 percent change in
        the maximum aggregate offering price set forth in the "Calculation of
        Registration Fee" table in the effective registration statement.
 
             (iii) To include any material information with respect to the plan
        of distribution not previously disclosed in the registration statement
        or any material change to such information in the registration
        statement;
 
provided, however, that paragraphs (a)(1)(i) and (a)(1)(ii) do not apply if the
registration statement is on Form S-3, Form S-8 or Form F-3, and the information
required to be included in a post-effective amendment by those paragraphs is
contained in periodic reports filed with or furnished to the Commission by the
registrant pursuant to Section 13 of 15(d) of the Securities Exchange Act of
1934 that are incorporated by reference in the registration statement.
 
          (2) That, for the purpose of determining any liability under the
     Securities Act of 1933, each such post-effective amendment shall be deemed
     to be a new registration statement relating to the securities offered
     therein, and the offering of such securities at that time shall be deemed
     to be the initial bona fide offering thereof.
 
          (3) To remove from registration by means of a post-effective amendment
     any of the securities being registered which remain unsold at the
     termination of the offering.
 
          (4) If the registrant is a foreign private issuer, to file a
     post-effective amendment to the registration statement to include any
     financial statements required by Rule 3-19 of this chapter at the start of
     any delayed offering or throughout a continuous offering. Financial
     statements and information otherwise required by Section 10(a)(3) of the
     Act need not be furnished, provided, that the registrant includes in the
     prospectus, by means of a post-effective amendment, financial statements
     required pursuant to this paragraph (a)(4) and other information necessary
     to ensure that all other information in the prospectus is at least as
     current as the date of those financial statements. Notwithstanding the
     foregoing, with respect to registration statements on Form F-3, a
     post-effective amendment need not be filed to include financial statements
     and information required by Section 10(a)(3) of the Act or Rule 3-19 of
     this chapter if such financial statements and information are contained in
     periodic reports filed with or furnished to the Commission by the
     registrant pursuant to Section 13 or Section 15(d) of the Securities
     Exchange Act of 1934 that are incorporated by reference in the Form F-3.
 
     (b) The undersigned registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act of 1933, each filing of the
registrant's annual report pursuant to Section 13(a) or Section 15(d) of the
Securities Exchange Act of 1934 (and, where applicable, each filing of any
employee benefit plan's annual report pursuant to Section 15(d) of the
Securities Act of 1934) that is incorporated by reference in this Registration
Statement shall be deemed to be a new registration statement relating to the
 
                                      II-2
<PAGE>   14
 
securities offered herein, and the offering of such securities at that time
shall be deemed to be the initial bona fide offering thereof.
 
     (c) Insofar as indemnification for liabilities arising under the Securities
Act of 1933 may be permitted to directors, officers and controlling persons of
the registrant pursuant to the provisions referred to in Item 15 hereof, or
otherwise, the registrant has been advised that in the opinion of the Securities
and Exchange Commission such indemnification is against public policy as
expressed in the Act and is, therefore, unenforceable. In the event that a claim
for indemnification against such liabilities (other than the payment by the
registrant of expenses incurred or paid by a director, officer or controlling
person of the registrant in the successful defense of any action, suit or
proceeding) is asserted by such director, officer or controlling person in
connection with the securities being registered, the registrant will, unless in
the opinion of its counsel the matter has been settled by controlling precedent,
submit to a court of appropriate jurisdiction the question whether such
indemnification by it is against public policy as expressed in the Act and will
be governed by the final adjudication of such issue.
 
                                      II-3
<PAGE>   15
 
                                   SIGNATURES
 
     Pursuant to the requirements of the Securities Act of 1933, as amended, the
registrant certifies that it has reasonable grounds to believe that it meets all
of the requirements for filing on Form S-3 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 May 14, 1998.
 
                                            LAMAR ADVERTISING COMPANY
 
                                            By:  /s/ KEVIN P. REILLY, JR.
 
                                              ----------------------------------
                                                     Kevin P. Reilly, Jr.
                                                President and Chief Executive
                                                            Officer
 
                               POWER OF ATTORNEY
 
     We, the undersigned officers and directors of Lamar Advertising Company
hereby severally constitute and appoint each of Kevin P. Reilly, Jr. and Keith
A. Istre our true and lawful attorneys, with full power to them in any and all
capacities, to sign any amendments to this Registration Statement on Form S-3
(including pre- and post-effective amendments), and any related Rule 462(b)
registration statement or amendment 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, as amended,
this Registration Statement has been signed by the following persons in the
capacities indicated on May 14, 1998.
 
<TABLE>
<CAPTION>
                      SIGNATURE                                     TITLE                    DATE
                      ---------                                     -----                    ----
<C>                                                      <S>                            <C>
 
              /s/ KEVIN P. REILLY, JR.
-----------------------------------------------------    Director and Principal
                Kevin P. Reilly, Jr.                       Executive Officer
 
                 /s/ KEITH A. ISTRE                      Director and Principal
-----------------------------------------------------      Financial and Accounting
                   Keith A. Istre                          Officer
 
                /s/ CHARLES W. LAMAR
-----------------------------------------------------
                  Charles W. Lamar                       Director
 
               /s/ GERALD H. MARCHAND
-----------------------------------------------------
                 Gerald H. Marchand                      Director
 
-----------------------------------------------------
                  Jack S. Rome, Jr.                      Director
 
-----------------------------------------------------
                 William R. Schmidt                      Director
 
             /s/ T. EVERETT STEWART, JR.
-----------------------------------------------------
               T. Everett Stewart, Jr.                   Director
</TABLE>
<PAGE>   16
 
                                 EXHIBIT INDEX
 
<TABLE>
<CAPTION>
        EXHIBIT
          NO.                                    DESCRIPTION
        -------                                  -----------
<C>                      <S>
           4.1           -- Amended and Restated Certificate of Incorporation of the
                            Registrant. Previously filed as Exhibit 3.1 to the
                            Registrant's Registration Statement on Form S-1 (File No.
                            333-05479), and incorporated herein by reference.
           4.2           -- By-Laws of the Registrant, as amended. Previously filed
                            as Exhibit 3.2 to the Registrant's Registration Statement
                            on Form S-1 (File No. 333-05479), and incorporated herein
                            by reference.
           5.1           -- Opinion of Palmer & Dodge LLP. Filed herewith.
          23.1           -- Consent of KPMG Peat Marwick LLP, independent accountants
                            of Lamar Advertising Company. Filed herewith.
          23.2           -- Consent of Philip R. Friedman & Associates, independent
                            accountants of Penn Advertising, Inc. Filed herewith.
          23.3           -- Consent of Coopers & Lybrand L.L.P., independent
                            accountants of National Advertising Company. Filed
                            herewith.
          23.4           -- Consent of Palmer & Dodge LLP (contained in Exhibit 5.1).
          24.1           -- Power of Attorney (included on the signature page of this
                            Registration Statement).
</TABLE>