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                                                                     EXHIBIT 4.2

                               SECOND AMENDMENT TO
                          SECURITIES PURCHASE AGREEMENT

         This Second Amendment (this "Amendment") to the Securities Purchase
Agreement (as amended, the "Securities Purchase Agreement"), dated as of April
3, 2001, between TeleCorp PCS, Inc., (the "Company"), a Delaware corporation and
Lucent Technologies Inc. ("Lucent"), is made as of this 21st day of September
2001 (the "Amendment Effective Date"), by and between the Company and Lucent.
Capitalized terms not otherwise defined herein shall have the meaning ascribed
thereto in the Securities Purchase Agreement. Any reference to a Section is,
unless otherwise specified, to a Section of the Securities Purchase Agreement.

         NOW, THEREFORE, for and in consideration of the mutual covenants and
agreements contained herein, and for good and valuable consideration, the
receipt and sufficiency of which is hereby acknowledged, the parties agree as
follows:

         1. Sections 1.1 (a) and (b) are amended to read in their entirety as
follows:

         (a) The following sales of Notes to be purchased by you shall take
place (each a "Closing") as follows: (i) on the Initial Closing Date (the "April
Closing") you shall purchase the Company's senior subordinated discount notes
with a yield of 11% yielding to the Company gross proceeds of $100,000,000 (the
"April Notes"), (ii) on the October Closing Date, you shall purchase the
Company's senior subordinated discount notes with a yield of 11% yielding to the
Company gross proceeds of $115,000,000 (the "October Notes"), (iii) on January
10, 2002, you shall purchase the Company's senior subordinated discount notes
with a yield equal to the lesser of (x) 12% and (y) 25 basis points below the
average of the closing sale yield for the TeleCorp Wireless, Inc. senior
subordinated discount notes due 2009 (the "Wireless Notes") as quoted by
Deutsche Banc Alex. Brown, Lehman Brothers, Inc. and J.P. Morgan-Chase (the
"Formula")
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over the five (5) trading days prior to January 10, 2002 yielding to the Company
gross proceeds of $100,000,000 (the "January Notes") and (iv) on April 15, 2002,
you shall purchase the Company's senior subordinated discount notes with a yield
equal to the Formula over the five (5) trading days prior to April 15, 2002
yielding to the Company gross proceeds of $110,000,000 (the "April 2002 Notes"
and together with the April Notes, the October Notes and the January Notes, the
"Notes"). Each Closing shall occur on the applicable Closing Date or such other
time as the Company and you may agree and at such location as the Company and
you may agree. Notwithstanding anything to the contrary contained herein the
Company, at its sole discretion, may determine not to sell some or all of the
Notes at any Closing.

                  (b)  Reserved.

            2.    The reference to Section 5.8 in Section 1.1(c) shall be
                  deleted.

            3.    Section 5.8 is amended to read in its entirety "Reserved."

            4.    Section 6 and 7 are amended to read in their entirety
                  "Reserved."

            5.    The following definition contained in Section 8 shall be
                  amended to read in its entirety as follows:

            Closing Date: the Initial Closing Date, the October Closing Date,
January 10, 2002 and April 15, 2002.

            6.    All references to Market Note Closing Date shall be deleted.

            7. Lucent as the current holder of all the Notes that are issued and
outstanding consents to an amendment to the Indenture to delete Section 6.01(10)
of the Indenture.

            8. Lucent agrees that it will not withdraw its consent to delete
Section 6.01(10) of the Indenture contained in Section 7 hereof.

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         9. The Company acknowledges that Lucent does not intend to manufacture
and support GSM and GPRS equipment and, accordingly, the Company and Lucent
acknowledge that the Procurement Contract applies in its entirety only to TDMA
equipment.

            10. Counterparts. This Amendment may be executed in multiple
counterparts, each of which shall be deemed to be an original and all of which
when taken together shall constitute one and the same agreement.

            11. GOVERNING LAW. THIS AMENDMENT SHALL BE CONSTRUED IN ACCORDANCE
WITH AND GOVERNED BY THE INTERNAL LAWS OF THE STATE OF NEW YORK APPLICABLE TO
AGREEMENTS MADE AND TO BE PERFORMED IN NEW YORK.

            IN WITNESS WHEREOF, the parties hereto have executed this Amendment
or caused it to be executed by their duly authorized officers all as of the
Amendment Effective Date.

                                  TELECORP PCS, INC.



                                  By: /s/ Thomas H. Sullivan
                                      ---------------------------------------
                                  Its: EVP and CFO


                                  LUCENT TECHNOLOGIES INC.



                                  By: /s/ Elizabeth Perricone
                                      ---------------------------------------
                                  Its: Director, Treasury