Hello again, supriyoch_2008,

I totally agree with tobyink that a hash is the superior option here. But, if you insist on using a 2-dimensional array, here is how to code it:

#! perl
use strict;
use warnings;
use Data::Dumper;

my @sample1 = qw/  a  b  c  d /;
my @sample2 = qw/  1  2  3  4 /;
my @sample3 = qw/ x1 x2 x3 x4 /;
my @big     = (\@sample1, \@sample2, \@sample3);    # <-- Note: use re
+ferences here!

print "Original big array:\n",  Dumper(@big),     "\n";

my $deleted_ele = 'x3';
remove(\@big, $deleted_ele);

print "Resultant big array:\n", Dumper(@big),     "\n";
print "Deleted element: $deleted_ele\n";
print "Modified sample1:\n",    Dumper(@sample1), "\n";
print "Modified sample2:\n",    Dumper(@sample2), "\n";
print "Modified sample3:\n",    Dumper(@sample3);

sub remove
{
    my ($array, $to_delete) = @_;

    for my $i (0 .. @$array - 1)
    {
        for my $j (0 .. @{$array->[$i]} - 1)
        {
            if ($array->[$i][$j] eq $to_delete)
            {
                splice @$array[$_], $j, 1 for 0 .. @$array - 1;    # <
+-- Can't use delete here
                return;
            }
        }
    }
}
[download]

18:05 >perl 579_SoPW.pl
Original big array:
$VAR1 = [
          'a',
          'b',
          'c',
          'd'
        ];
$VAR2 = [
          '1',
          '2',
          '3',
          '4'
        ];
$VAR3 = [
          'x1',
          'x2',
          'x3',
          'x4'
        ];

Resultant big array:
$VAR1 = [
          'a',
          'b',
          'd'
        ];
$VAR2 = [
          '1',
          '2',
          '4'
        ];
$VAR3 = [
          'x1',
          'x2',
          'x4'
        ];

Deleted element: x3
Modified sample1:
$VAR1 = 'a';
$VAR2 = 'b';
$VAR3 = 'd';

Modified sample2:
$VAR1 = '1';
$VAR2 = '2';
$VAR3 = '4';

Modified sample3:
$VAR1 = 'x1';
$VAR2 = 'x2';
$VAR3 = 'x4';

18:05 >
[download]

Compare this code to the solution given by tobyink, and it should be obvious that a hash is the way to go!

Hope that helps,

Update: Added 2 comments to the code.