<PAGE>   1
As filed with the Securities and Exchange Commission on April 7, 1999


                         Registration Statement No. 333-

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                 ---------------

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

                                 ---------------


                        Infinity Broadcasting Corporation
             (Exact name of Registrant as specified in its charter)

                     Delaware                                13-4030071
           (State or other jurisdiction                   (I.R.S. Employer
         of incorporation or organization)               Identification No.)


                               40 West 57th Street
                            New York, New York 10019
   (Address of Registrant's principal executive offices, including zip code)


           Infinity Broadcasting Corporation Stock Plan for Directors
                            (Full title of the plan)


                               ANGELINE C. STRAKA
                                    Secretary
                        Infinity Broadcasting Corporation
                               40 West 57th Street
                            New York, New York 10019
                     (Name and address of agent for service)
                                 (212) 975-3335
          (Telephone number, including area code, of agent for service)

                                 ---------------

                         CALCULATION OF REGISTRATION FEE

 Title of                          Proposed                           Proposed
securities         Amount           maximum           maximum         Amount of
   to be            to be        offering price      aggregate      registration
registered        registered       per share         offering           fee
                                      (1)               (1)              (1)
--------------------------------------------------------------------------------

Class A
Common Stock,
par value
$.01 per
share.......   250,000              $26.0625       $6,515,625          $1,811.34
--------------------------------------------------------------------------------

(1) Pursuant to Rule 457 under the Securities Act of 1933, the proposed maximum
aggregate offering price and the registration fee are based upon the average of
the high and low prices per share of the Registrant's Class A Common Stock
reported on the New York Stock Exchange Composite Tape on March 31, 1999.


                                      -1-
<PAGE>   2


                              EXPLANATORY STATEMENT

         This Registration Statement on Form S-8 registers 250,000 shares of
Class A Common Stock of Infinity Broadcasting Corporation ("Infinity"), par
value $.01 per share (the "Common Stock"), for issuance pursuant to the Infinity
Broadcasting Corporation Stock Plan for Directors (the "Plan").




                                      -2-
<PAGE>   3



                                     PART II

               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT


Item 3. Incorporation of Documents by Reference

     The following documents, each as filed by Infinity Broadcasting
Corporation, a Delaware corporation (the "Company" or "Infinity"), with the
Securities and Exchange Commission (the "Commission") are incorporated as of
their respective dates in this Registration Statement by reference:

         A. the Company's Annual Report on Form 10-K for the year ended December
31, 1998.

         B. the Description of Infinity's Class A Common Stock contained in
Infinity's Registration Statement on Form 8-A/A filed with the Commission on
November 5, 1998, as amended or updated pursuant to the Exchange Act.

         All documents subsequently filed by Infinity pursuant to Sections 13(a)
13(c), 14 or 15(d) of the Exchange Act prior to the filing of a post-effective
amendment to this Registration Statement which indicates that all securities
offered hereby have been sold or which deregisters all such securities then
remaining unsold shall be deemed to be incorporated by reference in this
Registration Statement by reference and to be a part hereof from the respective
date of filing of each such document. 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 Registration Statement
to the extent that a statement contained herein or in any other subsequently
filed document which also is or is deemed to be incorporated by reference herein
modifies or supersedes such statement. Any such statement so modified or
superseded shall not be deemed, except as so modified or superseded, to
constitute a part of this Registration Statement.

Item 4. Description of Securities

         Not applicable.

Item 5. Interests of Named Experts and Counsel

         Angeline C. Straka, Esquire, Secretary of the Company, has given an
opinion as to the legality of the securities being registered hereunder.

Item 6. Indemnification of Directors and Officers

         As permitted by applicable provisions of the Delaware General
Corporation Law ("DGCL"), the Restated Certificate contains a provision
eliminating, to the fullest extent permitted by the DGCL as it exists or may in
the future be amended, the liability of a director to Infinity and its
stockholders for monetary damages for breaches of fiduciary or other duty as a
director. However, the DGCL does not currently allow such provision to limit the
liability of a director for: (i) any breach of the director's duty of loyalty to
Infinity or its stockholders; (ii) acts or omissions not in good faith or which
involve intentional misconduct or a knowing violation of laws; (iii) payment of
dividends, stock purchases or redemptions that violate the DGCL; or (iv) any
transaction from which the director derived an improper personal benefit. Such
limitation of liability also does not affect the availability of equitable
remedies such as injunctive relief or rescission.

         The Restated Certificate and the By-Laws also provide that, to the
fullest extent permitted by the DGCL as it exists or may in the future be
amended, Infinity will indemnify and hold harmless any officer or director who
is or was made a party or is threatened to be made a party to or is involved in
any manner in any threatened, pending or completed action, suit or proceeding,
whether civil, criminal, administrative or investigative, by



                                      -3-
<PAGE>   4

reason of the fact that such person is or was an officer or director of
Infinity, and may indemnify any employee or agent of Infinity and any person
serving at the request of Infinity as a officer, director, partner, member,
employee or agent of another corporation, partnership, limited liability
company, joint venture, trust, employee benefit plan or other enterprise;
provided, however, that Infinity will indemnify any such person seeking
indemnification in connection with a proceeding (or part thereof) initiated by
such person only if such proceeding (or part thereof) was authorized by the
Board of Directors or is a proceeding to enforce such person's claim to
indemnification pursuant to the rights granted by the By-Laws. In addition,
Infinity will pay the expenses incurred by any officers and directors, and may
pay the expenses incurred by other persons that may be indemnified pursuant to
the Restated Certificate and the By-Laws, in defending any such proceeding in
advance of its final disposition upon receipt (unless Infinity upon
authorization of the Board of Directors waives such requirement to the extent
permitted by applicable law) of an undertaking by or on behalf of such person to
repay such amount if it is ultimately determined that such person is not
entitled to be indemnified by Infinity as authorized in the By-Laws or
otherwise. The Restated Certificate and the By-Laws also state that such
indemnification is not exclusive of any other rights of the indemnified party,
including rights under any indemnification agreements or otherwise.

         CBS Corporation currently maintains insurance on behalf of officers and
directors of CBS Corporation and its subsidiaries (including Infinity and its
subsidiaries) against any liability which may be asserted against any such
officer or director, subject to certain customary exclusions.

Item 7. Exemption from Registration Claimed

         Not applicable.

Item 8. Exhibits

      Exhibit No.     Description
      -----------     -----------

           4.1        Restated Certificate of Incorporation of Infinity as
                      amended to December 14, 1998, are incorporated by
                      reference to Exhibit 3.3 to Infinity's Registration
                      Statement No. 333-63727 on Form S-1, Amendment No. 4,
                      filed December 4, 1998.

           4.2        Restated By-laws of Infinity, as amended effective
                      December 14, 1998, are incorporated by reference to
                      Exhibit 3.4 to Infinity's Registration Statement No.
                      333-63727 on Form S-1, Amendment No. 4, filed December 4,
                      1998.

           4.3        Infinity Broadcasting Corporation Stock Plan for
                      Directors, effective as of December 14, 1998, is
                      incorporated by reference to Exhibit 10.25 to Company's
                      Annual Report on Form 10-K filed March 29, 1999.

           5          Opinion of Angeline C. Straka, Esquire, Secretary of the
                      Company, as to the legality of the securities.

           23.1       Consent of Counsel - contained in opinion filed as Exhibit
                      5.

           23.2       Consent of KPMG LLP.

           24         Powers of Attorney.




                                      -4-
<PAGE>   5

Item 9. Undertakings

         The undersigned Registrant hereby undertakes:

         (a) to file, during any period in which offers or sales are being made,
a post-effective amendment to this Registration Statement 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;

         (b) 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 offer thereof;

         (c) 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; and

         (d) 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 an employee benefit plan's annual report
pursuant to Section 15(d) of the Securities Exchange Act of 1934) that is
incorporated by reference in this Registration Statement 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:

         (e) 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 foregoing provisions, 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.

SIGNATURES

         Pursuant to the requirements of the Securities Act of 1933, the
Registrant, Infinity Broadcasting Corporation, 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 New York, State of
New York, on the 7th day of April, 1999.


                           Infinity Broadcasting Corporation


                           By:     /s/ Angeline C. Straka
                              -------------------------------------
                                       Angeline C. Straka
                                           Secretary



                                      -5-
<PAGE>   6


         Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons on the 7th day
of April, 1999, in the capacities indicated:

Signature                                            Title

                                    Chairman, President and
                 *                  Chief Executive Officer
---------------------------------   (principal executive officer)
(Mel Karmazin)                      and Director


                 *
---------------------------------   Director
(George H. Conrades)


                 *
---------------------------------   Director
(Richard R. Pivirotto)


                 *
---------------------------------   Director
(Jeffrey Sherman)


                 *
---------------------------------   Director
(Paula Stern)


                 *                  Executive Vice President, Chief
---------------------------------   Financial Officer and Treasurer
(Farid Suleman)                     (principal financial and accounting
                                    officer)and Director


                 *
---------------------------------   Director
(Robert D. Walter)





                                          *By /s/ Angeline C. Straka
                                             -----------------------
                                              Angeline C. Straka
                                              Secretary



                                      -6-
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1
As filed with the Securities and Exchange Commission on April 7, 1999

                         Registration Statement No. 333-

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                 ---------------

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

                                 ---------------

                        Infinity Broadcasting Corporation
             (Exact name of Registrant as specified in its charter)

                     Delaware                                13-4030071
           (State or other jurisdiction                   (I.R.S. Employer
         of incorporation or organization)               Identification No.)

                               40 West 57th Street
                            New York, New York 10019
   (Address of Registrant's principal executive offices, including zip code)

           Infinity Broadcasting Corporation Stock Plan for Directors
                            (Full title of the plan)

                               ANGELINE C. STRAKA
                                    Secretary
                        Infinity Broadcasting Corporation
                               40 West 57th Street
                            New York, New York 10019
                     (Name and address of agent for service)
                                 (212) 975-3335
          (Telephone number, including area code, of agent for service)

                                 ---------------

                         CALCULATION OF REGISTRATION FEE

 Title of                          Proposed                           Proposed
securities         Amount           maximum           maximum         Amount of
   to be            to be        offering price      aggregate      registration
registered        registered       per share         offering           fee
                                      (1)               (1)              (1)
--------------------------------------------------------------------------------

Class A
Common Stock,
par value
$.01 per
share.......   250,000              $26.0625       $6,515,625          $1,811.34
--------------------------------------------------------------------------------

(1) Pursuant to Rule 457 under the Securities Act of 1933, the proposed maximum
aggregate offering price and the registration fee are based upon the average of
the high and low prices per share of the Registrant's Class A Common Stock
reported on the New York Stock Exchange Composite Tape on March 31, 1999.

                                      -1-
2

                              EXPLANATORY STATEMENT

         This Registration Statement on Form S-8 registers 250,000 shares of
Class A Common Stock of Infinity Broadcasting Corporation ("Infinity"), par
value $.01 per share (the "Common Stock"), for issuance pursuant to the Infinity
Broadcasting Corporation Stock Plan for Directors (the "Plan").

                                      -2-
3

                                     PART II

               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT

Item 3. Incorporation of Documents by Reference

     The following documents, each as filed by Infinity Broadcasting
Corporation, a Delaware corporation (the "Company" or "Infinity"), with the
Securities and Exchange Commission (the "Commission") are incorporated as of
their respective dates in this Registration Statement by reference:

         A. the Company's Annual Report on Form 10-K for the year ended December
31, 1998.

         B. the Description of Infinity's Class A Common Stock contained in
Infinity's Registration Statement on Form 8-A/A filed with the Commission on
November 5, 1998, as amended or updated pursuant to the Exchange Act.

         All documents subsequently filed by Infinity pursuant to Sections 13(a)
13(c), 14 or 15(d) of the Exchange Act prior to the filing of a post-effective
amendment to this Registration Statement which indicates that all securities
offered hereby have been sold or which deregisters all such securities then
remaining unsold shall be deemed to be incorporated by reference in this
Registration Statement by reference and to be a part hereof from the respective
date of filing of each such document. 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 Registration Statement
to the extent that a statement contained herein or in any other subsequently
filed document which also is or is deemed to be incorporated by reference herein
modifies or supersedes such statement. Any such statement so modified or
superseded shall not be deemed, except as so modified or superseded, to
constitute a part of this Registration Statement.

Item 4. Description of Securities

         Not applicable.

Item 5. Interests of Named Experts and Counsel

         Angeline C. Straka, Esquire, Secretary of the Company, has given an
opinion as to the legality of the securities being registered hereunder.

Item 6. Indemnification of Directors and Officers

         As permitted by applicable provisions of the Delaware General
Corporation Law ("DGCL"), the Restated Certificate contains a provision
eliminating, to the fullest extent permitted by the DGCL as it exists or may in
the future be amended, the liability of a director to Infinity and its
stockholders for monetary damages for breaches of fiduciary or other duty as a
director. However, the DGCL does not currently allow such provision to limit the
liability of a director for: (i) any breach of the director's duty of loyalty to
Infinity or its stockholders; (ii) acts or omissions not in good faith or which
involve intentional misconduct or a knowing violation of laws; (iii) payment of
dividends, stock purchases or redemptions that violate the DGCL; or (iv) any
transaction from which the director derived an improper personal benefit. Such
limitation of liability also does not affect the availability of equitable
remedies such as injunctive relief or rescission.

         The Restated Certificate and the By-Laws also provide that, to the
fullest extent permitted by the DGCL as it exists or may in the future be
amended, Infinity will indemnify and hold harmless any officer or director who
is or was made a party or is threatened to be made a party to or is involved in
any manner in any threatened, pending or completed action, suit or proceeding,
whether civil, criminal, administrative or investigative, by

                                      -3-
4

reason of the fact that such person is or was an officer or director of
Infinity, and may indemnify any employee or agent of Infinity and any person
serving at the request of Infinity as a officer, director, partner, member,
employee or agent of another corporation, partnership, limited liability
company, joint venture, trust, employee benefit plan or other enterprise;
provided, however, that Infinity will indemnify any such person seeking
indemnification in connection with a proceeding (or part thereof) initiated by
such person only if such proceeding (or part thereof) was authorized by the
Board of Directors or is a proceeding to enforce such person's claim to
indemnification pursuant to the rights granted by the By-Laws. In addition,
Infinity will pay the expenses incurred by any officers and directors, and may
pay the expenses incurred by other persons that may be indemnified pursuant to
the Restated Certificate and the By-Laws, in defending any such proceeding in
advance of its final disposition upon receipt (unless Infinity upon
authorization of the Board of Directors waives such requirement to the extent
permitted by applicable law) of an undertaking by or on behalf of such person to
repay such amount if it is ultimately determined that such person is not
entitled to be indemnified by Infinity as authorized in the By-Laws or
otherwise. The Restated Certificate and the By-Laws also state that such
indemnification is not exclusive of any other rights of the indemnified party,
including rights under any indemnification agreements or otherwise.

         CBS Corporation currently maintains insurance on behalf of officers and
directors of CBS Corporation and its subsidiaries (including Infinity and its
subsidiaries) against any liability which may be asserted against any such
officer or director, subject to certain customary exclusions.

Item 7. Exemption from Registration Claimed

         Not applicable.

Item 8. Exhibits

      Exhibit No.     Description
      -----------     -----------

           4.1        Restated Certificate of Incorporation of Infinity as
                      amended to December 14, 1998, are incorporated by
                      reference to Exhibit 3.3 to Infinity's Registration
                      Statement No. 333-63727 on Form S-1, Amendment No. 4,
                      filed December 4, 1998.

           4.2        Restated By-laws of Infinity, as amended effective
                      December 14, 1998, are incorporated by reference to
                      Exhibit 3.4 to Infinity's Registration Statement No.
                      333-63727 on Form S-1, Amendment No. 4, filed December 4,
                      1998.

           4.3        Infinity Broadcasting Corporation Stock Plan for
                      Directors, effective as of December 14, 1998, is
                      incorporated by reference to Exhibit 10.25 to Company's
                      Annual Report on Form 10-K filed March 29, 1999.

           5          Opinion of Angeline C. Straka, Esquire, Secretary of the
                      Company, as to the legality of the securities.

           23.1       Consent of Counsel - contained in opinion filed as Exhibit
                      5.

           23.2       Consent of KPMG LLP.

           24         Powers of Attorney.

                                      -4-
5

Item 9. Undertakings

         The undersigned Registrant hereby undertakes:

         (a) to file, during any period in which offers or sales are being made,
a post-effective amendment to this Registration Statement 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;

         (b) 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 offer thereof;

         (c) 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; and

         (d) 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 an employee benefit plan's annual report
pursuant to Section 15(d) of the Securities Exchange Act of 1934) that is
incorporated by reference in this Registration Statement 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:

         (e) 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 foregoing provisions, 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.

SIGNATURES

         Pursuant to the requirements of the Securities Act of 1933, the
Registrant, Infinity Broadcasting Corporation, 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 New York, State of
New York, on the 7th day of April, 1999.

                           Infinity Broadcasting Corporation

                           By:     /s/ Angeline C. Straka
                              -------------------------------------
                                       Angeline C. Straka
                                           Secretary

                                      -5-
6

         Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed by the following persons on the 7th day
of April, 1999, in the capacities indicated:

Signature                                            Title

                                    Chairman, President and
                 *                  Chief Executive Officer
---------------------------------   (principal executive officer)
(Mel Karmazin)                      and Director

                 *
---------------------------------   Director
(George H. Conrades)

                 *
---------------------------------   Director
(Richard R. Pivirotto)

                 *
---------------------------------   Director
(Jeffrey Sherman)

                 *
---------------------------------   Director
(Paula Stern)

                 *                  Executive Vice President, Chief
---------------------------------   Financial Officer and Treasurer
(Farid Suleman)                     (principal financial and accounting
                                    officer)and Director

                 *
---------------------------------   Director
(Robert D. Walter)

                                          *By /s/ Angeline C. Straka
                                             -----------------------
                                              Angeline C. Straka
                                              Secretary

                                      -6-