<PAGE>   1
                                    FORM 10-Q

                       SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549


              [X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

               FOR THE QUARTERLY PERIOD ENDED: SEPTEMBER 30, 1996
                                       OR

              [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
                         SECURITIES EXCHANGE ACT OF 1934
             FOR THE TRANSACTION PERIOD FROM__________TO __________.

COMMISSION FILE NUMBER:  1-13560


                       CORRECTIONS CORPORATION OF AMERICA
             (Exact name of Registrant as specified in its charter)

                    DELAWARE                              62-1156308
    ----------------------------------------    -----------------------------
        (State or other jurisdiction of                (I.R.S. Employer
         incorporation or organization)             Identification Number)

         102 WOODMONT BLVD., SUITE 800
              NASHVILLE, TENNESSEE                          37205
    ----------------------------------------    -----------------------------
    (Address of principal executive offices)              (Zip Code)


                                 (615) 292-3100
--------------------------------------------------------------------------------
              (Registrant's telephone number, including area code)

                                      NONE
--------------------------------------------------------------------------------
      (Former name, address and fiscal year if changed since last report.)



Indicate by check mark whether the Registrant (1) has filed all reports required
to be filed by Section 13 or 15 (d) of the Securities Exchange Act of 1934
during the preceding 12 months (or for such shorter period that the Registrant
was required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.
Yes _X_ No ____

                                   74,928,848
--------------------------------------------------------------------------------
    (Outstanding shares of the issuer's common stock as of November 1, 1996.)


                            EXHIBIT INDEX ON PAGE 11

               Total number of sequentially numbered pages is 12.
<PAGE>   2
                       CORRECTIONS CORPORATION OF AMERICA

                                      INDEX



                                                                        Page
PART I. FINANCIAL INFORMATION:                                         Number
                                                                       ------
 Item 1. Financial Statements

         Consolidated Balance Sheets
         September 30, 1996 (Unaudited) and December 31, 1995              3

         Consolidated Statements of Operations
         Nine months ended September 30, 1996 and 1995
         (Unaudited)                                                       4

         Consolidated Statements of Operations
         Three months ended September 30, 1996 and 1995
         (Unaudited)                                                       5

         Consolidated Statements of Cash Flows
         Nine months ended September 30, 1996 and 1995
         (Unaudited)                                                     6-7

         Notes to Consolidated Financial Statements
         (Unaudited)                                                       8

 Item 2. Management's Discussion and Analysis of Financial
         Condition and Results of Operations                            9-10


PART II.  OTHER INFORMATION

 Item 1. Legal Proceedings                                                11

 Item 2. Changes in Securities                                            11

 Item 3. Default Upon Senior Securities                                   11

 Item 4. Submission of Matters to a Vote of Security Holders              11

 Item 5. Other Information                                                11

 Item 6. Exhibits and Reports on Form 8-K                                 11


                                                                               2
<PAGE>   3
               CORRECTIONS CORPORATION OF AMERICA AND SUBSIDIARIES

                           CONSOLIDATED BALANCE SHEETS
                                 (in thousands)

<TABLE>
<CAPTION>
                                                  September 30,     December 31,
                                                       1996             1995
                                                  -------------     ------------
                                                   (Unaudited)
<S>                                                 <C>              <C>      
ASSETS
Current assets:
   Cash, cash equivalents and restricted cash       $  84,234        $   2,714
   Accounts receivable                                 58,991           39,661
   Prepaid expenses                                     3,388            1,569
   Deferred taxes                                       1,218            1,646
   Other                                                1,420            1,020
                                                    ---------        ---------
      Total current assets                            149,251           46,610
                                                    ---------        ---------
Restricted investments                                    587              443
Other assets                                           27,875           19,642
Property and equipment, net                           231,567          137,019
Investment in direct financing lease                   13,021            9,764
                                                    ---------        ---------
                                                    $ 422,301        $ 213,478
                                                    =========        =========
LIABILITIES AND STOCKHOLDERS' EQUITY

Current liabilities:
   Accounts payable                                 $  30,895        $  10,757
   Accrued salaries and wages                           5,006            3,480
   Accrued property taxes                               1,630            1,623
   Other accrued expenses                               8,988            8,637
   Current portion of long-term debt                   10,674           11,020
                                                    ---------        ---------
      Total current liabilities                        57,193           35,517
                                                    ---------        ---------
Long-term debt, net of current portion                 90,765           74,865
Deferred taxes                                          4,334            4,164
Other long-term liabilities                             1,485            2,228
                                                    ---------        ---------
      Total liabilities                               153,777          116,774
                                                    ---------        ---------
Stockholders' equity:
   Common stock - $1 par value                         74,775           64,540
   Additional paid-in capital                         161,572           16,560
   Retained earnings                                   32,426           15,641
   Treasury stock, at cost                               (249)             (37)
                                                    ---------        ---------
      Total stockholders' equity                      268,524           96,704
                                                    ---------        ---------
                                                    $ 422,301        $ 213,478
                                                    =========        =========
</TABLE>


                                                                               3
<PAGE>   4
               CORRECTIONS CORPORATION OF AMERICA AND SUBSIDIARIES

                      CONSOLIDATED STATEMENTS OF OPERATIONS
                                   (Unaudited)
                      (in thousands, except per share data)

<TABLE>
<CAPTION>
                                                           Nine months ended
                                                              September 30
                                                        ------------------------
                                                          1996            1995
                                                        --------        --------
<S>                                                     <C>             <C>     
Revenues                                                $205,933        $144,911

Expenses:
   Operating                                             151,440         111,897
   General and administrative                              9,811          10,793
   Depreciation and amortization                           7,030           4,453
                                                        --------        --------
                                                         168,281         127,143
                                                        --------        --------
Contribution from operations                              37,652          17,768
Interest expense, net                                      3,293           2,707
                                                        --------        --------
Income before income taxes                                34,359          15,061
Provision for income taxes                                13,186           5,897
                                                        --------        --------
Net income                                              $ 21,173        $  9,164
                                                        ========        ========
Net income per common share:
   Primary                                              $   0.26        $   0.13
                                                        ========        ========
   Fully diluted                                        $   0.25        $   0.12
                                                        ========        ========
Weighted average common shares outstanding:               82,270          74,559
                                                        ========        ========
</TABLE>


                                                                               4
<PAGE>   5
               CORRECTIONS CORPORATION OF AMERICA AND SUBSIDIARIES

                      CONSOLIDATED STATEMENTS OF OPERATIONS
                                   (Unaudited)
                      (in thousands, except per share data)

<TABLE>
<CAPTION>
                                                           Three months ended
                                                               September 30
                                                         -----------------------
                                                           1996            1995
                                                         -------         -------
<S>                                                      <C>             <C>    
Revenues                                                 $75,203         $49,515

Expenses:
   Operating                                              54,931          36,290
   General and administrative                              3,517           4,284
   Depreciation and amortization                           2,489           1,537
                                                         -------         -------
                                                          60,937          42,111
                                                         -------         -------
Contribution from operations                              14,266           7,404
Interest expense, net                                        763           1,046
                                                         -------         -------
Income before income taxes                                13,503           6,358
Provision for income taxes                                 5,043           2,341
                                                         -------         -------
Net income                                               $ 8,460         $ 4,017
                                                         =======         =======
Net income per common share:
   Primary                                               $  0.10         $  0.06
                                                         =======         =======
   Fully diluted                                         $  0.10         $  0.05
                                                         =======         =======
Weighted average common shares outstanding:               84,603          77,196
                                                         =======         =======
</TABLE>


                                                                               5
<PAGE>   6
               CORRECTIONS CORPORATION OF AMERICA AND SUBSIDIARIES

                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                   (Unaudited)
                                 (in thousands)

<TABLE>
<CAPTION>
                                                                   Nine months ended
                                                                      September 30
                                                                 ----------------------
                                                                    1996         1995
                                                                 ---------     --------
<S>                                                              <C>           <C>     
Cash Flows from Operating Activities:
   Net income                                                    $  21,173     $  9,164
   Adjustments to reconcile net income to net cash provided
       by operating activities:
          Depreciation and amortization                              7,029        4,456
          Deferred income taxes                                      9,742        3,549
          Loss on disposal of property and equipment                    19            7
          Equity in earnings of unconsolidated entities               (650)        (526)
          Changes in assets and liabilities:
               Accounts receivable                                 (19,222)     (11,389)
               Prepaid expenses                                     (1,819)        (388)
               Other current assets                                   (400)        (250)
               Accounts payable                                     20,138        8,303
               Accrued expenses                                      1,988        2,520
                                                                 ---------     --------
                   Net cash provided by operating activities        37,998       15,446
                                                                 ---------     --------
Cash Flows from Investing Activities:
   Increase in restricted and escrow cash                           (2,496)         (36)
   Increase in restricted investments                                 (144)        (518)
   Increase in other assets                                         (9,547)     (26,568)
   Acquisition of property and equipment                          (106,179)     (21,847)
   Proceeds from disposals of property and equipment                 6,533           45
   Increase in direct financing lease                               (3,693)         -0-
   Payments received on direct financing lease and notes
          receivable                                                   342          235
                                                                 ---------     --------
                   Net cash used in investing activities          (115,184)     (48,689)
                                                                 ---------     --------
Cash Flows from Financing Activities:
   Proceeds from issuance of long-term debt                         50,000        7,604
   Payments on long-term debt                                      (19,300)      (5,549)
   Proceeds from payments on line of credit, net                   (15,146)       2,416
   Payments of short-term obligations refinanced by long-term
        debt                                                           -0-       17,480
   Payment of debt issuance costs                                     (743)        (495)
   Issuance of common stock                                        138,750        8,683
   Payments of stock issuance costs                                 (6,939)         -0-
   Proceeds from exercise of stock options and warrants              9,588          350
   Repurchase of stock warrants                                        -0-         (630)
                                                                 ---------     --------
                   Net cash provided by financing activities       156,210       29,859
                                                                 ---------     --------
</TABLE>


                                                                               6
<PAGE>   7
               CORRECTIONS CORPORATION OF AMERICA AND SUBSIDIARIES

                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                   (Unaudited)
                                 (in thousands)

<TABLE>
<CAPTION>
                                                                 Nine months ended
                                                                    September 30
                                                                ---------------------
                                                                  1996         1995
                                                                --------     --------
<S>                                                             <C>          <C>     
Net increase (decrease) in cash                                   79,024       (3,384)
                                                                --------     --------
CASH AND CASH EQUIVALENTS, beginning of period                     2,145        4,285
                                                                --------     --------
CASH AND CASH EQUIVALENTS, end of period                        $ 81,169     $    901
                                                                ========     ========
Supplemental Disclosures of Cash Flow Information:

   Cash paid during the period for:
       Interest                                                 $  4,984     $  2,843
                                                                ========     ========
       Income taxes                                             $  2,978     $  2,516
                                                                ========     ========
Supplemental Schedule of Noncash Investing and Financing
   Activities:

       The Company acquired property and equipment by
           assuming long-term debt:
             Property and equipment                             $      0     $ 27,392
             Long-term debt                                            0      (27,392)
                                                                --------     --------
                                                                $      0     $      0
                                                                ========     ========
       Long-term debt was converted into common stock:
             Other assets                                       $      0     $    (53)
             Long-term debt                                            0        6,700
             Common stock                                              0         (444)
             Additional paid-in capital                                0       (6,203)
                                                                --------     --------
                                                                $      0     $      0
                                                                ========     ========
       The Company acquired treasury stock and issued common
           stock through the exercise of stock options:
             Common stock                                       $ (1,026)    $   (234)
             Additional paid-in capital                           (2,400)        (681)
             Retained earnings                                     3,129          540
             Treasury stock, at cost                                 297          375
                                                                --------     --------
                                                                $      0     $      0
                                                                ========     ========
</TABLE>


                                                                               7
<PAGE>   8
               CORRECTIONS CORPORATION OF AMERICA AND SUBSIDIARIES

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                   (Unaudited)


1.    CONSOLIDATED FINANCIAL STATEMENTS

      The consolidated balance sheets as of September 30, 1996 and December
      1995, the consolidated statements of operations and cash flows for the
      nine month periods ended September 30, 1996 and 1995, and the consolidated
      statements of operations for the quarters ended September 30, 1996 and
      1995 have been prepared by the Company in accordance with the accounting
      policies described in its 1995 Annual Report and should be read in
      conjunction with the notes thereto.

      In the opinion of management, all adjustments (which include only normal
      recurring adjustments) necessary to present fairly the financial
      positions, results of operations and changes in cash flows at September
      30, 1996 and for all periods presented have been made.

      Certain information and footnote disclosures normally included in
      financial statements prepared in accordance with generally accepted
      accounting principles have been condensed or omitted. The results of
      operations for the period ended September 30, 1996, are not necessarily
      indicative of the operating results for the full year.

      Certain reclassifications of 1995 amounts have been made to conform with
      the 1996 presentation.

2.    LONG-TERM DEBT

      In February, 1996, the Company sold $30,000,000 of convertible
      subordinated notes. The notes bear interest at 7.5%, payable quarterly and
      mature in 2002. The Company used the proceeds to repay the principal
      outstanding under the Company's bank loan and line of credit, $12,353,000
      and $17,000,000 respectively.

      In April, 1996, as a result of its preemptive right triggered in
      connection with the issuance of convertible subordinated notes, the
      Company sold $20,000,000 of convertible subordinated notes to Sodexho,
      S.A. with terms identical to the aforementioned notes. The proceeds were
      used to fund construction of facility expansions.

3.    STOCKHOLDERS' EQUITY

      In June, 1996, the Company completed a public offering of 1,850,000 shares
      of common stock at a price to the public of $75.00 per share. The proceeds
      of the offering, after deducting all associated costs, were $131,948,000.

      Also in June, 1996, the Company announced a two-for-one stock split to be
      effected in the form of a stock dividend. The dividend was distributed on
      July 2, 1996, to all shareholders of record on June 19, 1996. The
      consolidated balance sheet and consolidated statements of operations and
      cash flows, as well as all earnings per share data, are reflective of the
      dividend.


                                                                               8
<PAGE>   9
Item 2.     MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
            RESULTS OF OPERATIONS

      RESULTS OF OPERATIONS

      REVENUES AND EXPENSES FROM OPERATIONS

      Revenues for the third quarter and first nine months of 1996 increased 52%
      and 42%, respectively, over the comparable periods of 1995. Management
      revenues increased $25,544,000 and $60,133,000 for the third quarter and
      first nine months of 1996, respectively, as compared to the same periods
      of 1995, while transportation revenues increased $144,000 and $889,000 for
      the same relative time periods. The increase in management revenues was
      due to compensated mandays increasing by 57% and 52% for third quarter and
      first nine months of 1996, respectively, over the comparable periods of
      1995. Through a series of new facility openings and existing facility
      expansions during 1995 and 1996, the Company added approximately 6,600
      beds to the domestic operations. These additional beds are reflected in
      1996 revenues as compared to 1995. The 6% and 13% increase in
      transportation revenues for the third quarter and nine months of 1996,
      respectively, over the comparable periods of 1995 was due to a marketing
      effort resulting in an expanded customer base and therefore increased
      compensated mileage.

      Operating expenses, while increasing in dollar amount 49% and 35% for the
      third quarter and first nine months of 1996, respectively, as compared to
      the same periods of 1995, actually decreased as a percentage of revenue
      for both periods. As more beds have been brought on line, the Company has
      been able to realize more economies of scale and in effect bring operating
      expenses down as a percentage of revenues. During 1996, the Company has
      been able to further integrate the facilities acquired in 1995 into the
      Company's operational systems.

      General and administrative expenses for the third quarter and first nine
      months of 1996 decreased 18% and 9% respectively, over the comparable
      periods of 1995. This decrease is due to the pooling expenses associated
      with acquisitions in the 1995 periods as well as the Company's ability to
      reduce duplication in the general and administrative areas by integrating
      the acquired facilities into its systems. As the Company continues to
      grow, general and administrative expenses should grow in volume but
      continue to decrease as a percentage of revenues.

      Depreciation and amortization for the third quarter and first nine months
      of 1996 increased 62% and 58% respectively, over the comparable periods of
      1995. This increase was a result of the Company expanding five of its
      owned facilities by a total of 1,350 beds.

      OTHER EXPENSES

      Interest expense, net, decreased 27% for the third quarter and increased
      22% for the first nine months of 1996, respectively, as compared to the
      same periods in 1995. The increase for the nine month period is the result
      of an additional $50,000,000 in convertible, subordinated debt funded in
      February and April, 1996. The decrease in the third quarter is due to a
      significant increase in interest income as the Company had approximately
      $104,000,000 in cash on average for the quarter from the secondary
      offering.


                                                                               9
<PAGE>   10
      FINANCIAL CONDITION, LIQUIDITY AND CAPITAL RESOURCES

      The Company's business is capital intensive in relation to the development
      of a correctional facility. The Company's efforts to obtain contracts,
      construct additional facilities and maintain its day-to-day operations
      have required the continued acquisition of funds through borrowings and
      equity offerings. The Company has financed these activities through the
      sale of capital stock, subordinated convertible notes and senior secured
      debt, through the issuance of taxable and tax-exempt bonds, by bank
      borrowings, and by assisting governmental agencies in the issuance of
      municipal bonds.

      Cash flow from operations for the first nine months of 1996 was
      $37,998,000 as compared to $15,446,000 for the comparable period in 1995.
      The Company has strengthened its cash flow through its expanded business,
      additional focus on larger, more profitable facilities, the expansion of
      existing facilities where economies of scale can be realized, and the
      continuing effort of cost containment. Cash flow from operations has
      allowed the Company to fund growth and to continue to retire debt on an
      accelerated basis.

      In September, 1996, the Company entered into a new credit facility with a
      group of banks which expanded its capacity from $25,000,000 to
      $170,000,000. The credit facility provides for general corporate
      borrowings and the issuance of a maximum of $136,000,000 in letters of
      credit. The credit facility bears interest, at the election of the
      Company, at either the bank's prime rate or a rate which is .5% above the
      applicable 30, 60 or 90 day LIBOR rate. Interest is payable quarterly with
      respect to prime rate loans and at the expiration of the applicable LIBOR
      period with respect to LIBOR rate based loans. There are no prepayment
      penalties associated with the credit facility. The credit facility
      requires the Company, among other things, to maintain maximum leverage
      ratios and a minimum debt service coverage ratio. The facility also limits
      certain payments and distributions. As of September 30, 1996, there were
      no borrowings under the facility. Letters of Credit totaling $28,250,000
      have been issued leaving the unused commitment at $141,750,000.

      In September, 1996, the Company also closed a $2,500,000 credit facility
      with a bank which provides for the issuance of letters of credit. As of
      September 30, 1996 there were $1,377,000 in letters of credit issued
      leaving the unused commitment at $1,123,000.

      In February, 1996, the Company issued $30,000,000 of its convertible
      subordinated notes to an investor. The proceeds were used to repay the
      outstanding principal, at the date of funding, under the Company's working
      capital credit facility and construction loan. The notes bear interest at
      7.5%, are payable quarterly and require the Company to maintain specific
      ratio requirements relating to net worth, cash flow and debt coverage. In
      April, 1996, as a result of its preemptive right triggered in connection
      with the issuance of convertible subordinated notes, Sodexho, S.A., an
      affiliate of the Company, acquired $20,000,000 of convertible subordinated
      notes under the same terms and conditions.

      The Company anticipates making cash investments in connection with future
      acquisitions and expansions. In addition, in accordance with the
      developing trend of private prison manages toward making strategic
      financial investments in facilities, the Company plans to use a portion of
      its cash to finance start-up costs, leasehold improvements and equity
      investments in facilities, if appropriate, in connection with undertaking
      new contracts. The Company believes that the cash flow from operations,
      proceeds from the secondary offering and amounts available under its
      credit facility will be sufficient to meet its capital requirements for
      the foreseeable future. Furthermore, management believes that additional
      resources may be available to the Company through a variety of other
      financing methods.


                                                                              10
<PAGE>   11
      PART II - OTHER INFORMATION



      Item 1.  Legal Proceedings

               None

      Item 2.  Changes in Securities

               None

      Item 3.  Default Upon Senior Securities

               None

      Item 4.  Submission of Matters to a Vote of Security Holders

               None

      Item 5.  Other Information

               None

      Item 6.  Exhibits and Reports on Form 8-K

               a) 27    Financial Data Schedule (for SEC use only)
               b) None


                                                                              11
<PAGE>   12
                                   SIGNATURES




Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.


                                      CORRECTIONS CORPORATION OF AMERICA
                                             (Registrant)




       November 12, 1996                  /s/ Darrell K. Massengale
-----------------------------------  -------------------------------------------
          (Date)                                   Darrell K. Massengale
                                                               Treasurer
                                          (Principal Accounting Officer)


                                                                              12