Or if you don't wish to read the whole file into memory, you can always just read in a section:

#!/usr/bin/perl

use strict;
use warnings;

my %res;
{ # for localizing $/
local $/ = 'END_TAG';
/BEGIN_TAG_(\d+)(.*)END_TAG/s and $res{$1} = $2 while <DATA>;
}
use Data::Dump 'dd'; dd \%res;

__DATA__
Any text is in this document.
But I'm only interested in the text between a beginning and an end tag
+.
BEGIN_TAG_110
In this text I'm interested in.
It can consist of several lines. Until the end tag.
END_TAG and any other things I'm not interested in until the next begi
+nning tag starts.
Any other text.
BEGIN_TAG_237
I need this text.
END_TAG
More text ...
[download]

Outputs:

{
  110 => "\nIn this text I'm interested in.\nIt can consist of several
+ lines. Until the end tag.\n",
  237 => "\nI need this text.\n",
}
[download]