<PAGE>   1

                                                                      EXHIBIT 11

                      LAIDLAW ENVIRONMENTAL SERVICES, INC.
                 STATEMENT OF COMPUTATION OF PER SHARE EARNINGS
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                                 Three Months Ended November 30,
                                                                 -------------------------------
                                                                     1997             1996
                                                                   --------         --------
<S>                                                                <C>              <C>     
Primary:
      Income from continuing operations                            $ 10,144         $  3,588
      Income from discontinued operations                              --                703
                                                                   --------         --------
      Primary net income                                           $ 10,144         $  4,291
                                                                   ========         ========

      Weighted average common stock outstanding (000s)              180,729          120,000
      Dilutive stock options                                             93             --
                                                                   --------         --------
      Primary weighted average common stock
          and common stock equivalents outstanding                  180,822          120,000
                                                                   ========         ========

      Income per share from continuing operations                  $  0.056         $  0.030
      Income per share from discontinued operations                    --              0.006
                                                                   --------         --------
      Primary net income per share                                 $  0.056         $  0.036
                                                                   ========         ========


Fully diluted:
      Primary income from continuing operations                    $ 10,144         $  3,588
      Add back: interest expense on conversion
                of subordinated convertible debenture                 2,625             --
                                                                   --------         --------
      Fully diluted income from continuing operations              $ 12,769         $  3,588
                                                                   ========         ========

      Primary income from discontinued operations                  $   --           $    703
                                                                   --------         --------
      Fully diluted income from discontinued operations            $   --           $    703
                                                                   ========         ========


      Primary shares outstanding (000s)                             180,822          120,000
      Dilutive effect of conversion of $350,000,000
          subordinated convertible debenture at $3.75                93,334             --
                                                                   --------         --------
      Fully diluted average shares outstanding                      274,156          120,000
                                                                   ========         ========

      Income per share from continuing operations                  $  0.047         $  0.030
      Income per share from discontinued operations                    --              0.006
                                                                   --------         --------
      Fully diluted net income per share                           $  0.047         $  0.030
                                                                   ========         ========
</TABLE>