<PAGE>   1


                      Laidlaw Environmental Services, Inc.
                 Statement of Computation of Per Share Earnings
                                   Exhibit 11
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                              Three Months Ended            Six Months Ended
                                                                 February 28,                  February 28,
                                                            -----------------------      ------------------------
                                                              1998           1997           1998           1997
                                                            --------      ---------       --------      ---------
<S>                                                         <C>           <C>             <C>           <C>      
Basic:
      Income from continuing operations                     $  3,556      $   1,750       $ 13,700      $   5,338
      Income from discontinued operations                       --             (917)          --             (214)
                                                            --------      ---------       --------      ---------
      Income available to common stockholders               $  3,556      $     833       $ 13,700      $   5,124
                                                            ========      =========       ========      =========

      Weighted average common stock outstanding (000s)       182,283        120,000        181,523        120,000
                                                            ========      =========       ========      =========

      Income per share from continuing operations           $  0.020      $   0.015       $  0.075      $   0.044
      Income per share from discontinued operations             --           (0.008)          --           (0.002)
                                                            --------      ---------       --------      ---------
      Basic income per share                                $  0.020      $   0.007       $  0.075      $   0.042
                                                            ========      =========       ========      =========


Diluted:
      Income from continuing operations                     $  3,556      $   1,750       $ 13,700      $   5,338
      Add back: interest expense on conversion
          of subordinated convertible debenture                 --             --            5,171           --
                                                            --------      ---------       --------      ---------
      Income available to common stockholders,
          plus assumed conversions                          $  3,556      $   1,750       $ 18,871      $   5,338
                                                            ========      =========       ========      =========

      Income from discontinued operations                   $   --        $    (917)      $   --        $    (214)
                                                            ========      =========       ========      =========
      Diluted income from discontinued operations           $   --        $    (917)      $   --        $    (214)
                                                            ========      =========       ========      =========


      Weighted average common stock outstanding (000s)       182,283        120,000        181,523        120,000
      Dilutive effect of stock options                           359           --              450           --
      Dilutive effect of conversion of $350,000,000
          subordinated convertible debenture at $3.75           --             --           93,333           --
                                                            --------      ---------       --------      ---------
      Diluted average shares outstanding                     182,642        120,000        275,306        120,000
                                                            ========      =========       ========      =========

      Income per share from continuing operations           $  0.019      $   0.015       $  0.069      $   0.044
      Income per share from discontinued operations             --           (0.008)          --           (0.002)
                                                            --------      ---------       --------      ---------
      Diluted net income per share                          $  0.019      $   0.007       $  0.069      $   0.042
                                                            ========      =========       ========      =========

</TABLE>