Break up the elements and sort on the two fragments: 
#!/usr/bin/perl
use strict;
use warnings;
use Data::Dumper 'Dumper';

my @files = qw(firstcase_1 firstcase_2 firstcase_10 secondcase_4 secon
+dcase_1 secondcase_11);

my @sorted = sort { $a =~ /^(\w+)_(\d+)$/; my ($a1,$a2) = ($1,$2);
                    $b =~ /^(\w+)_(\d+)$/; my ($b1,$b2) = ($1,$2);
                    $a1 cmp $b1 || $a2 <=> $b2 }
             @files;

print Dumper(\@sorted);

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In reply to Re: sorting numerically and alphabetically by cLive ;-)
in thread sorting numerically and alphabetically by kepster

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