Almost the same as shmem, but I thought I'd use "</TABLE>" as the record separator. That gives you one extra record at the end, which you can easily ignore, but works if you don't have "\n\n". Or flip-flop; or slurp-n-split.

use strict;
my $line = '='x60 ."\n";
#&RS;
⃜
#&SlurpAndSplit;
sub RS {
   $/=q{</TABLE>};
   while (<DATA>){
      if (s|\s*<TABLE (.+?)>|$1|) {
         chomp;
         print $line.$_;
      }
   }
}

sub SlurpAndSplit {
   $/=undef;
   chomp(my @tables = split(/<\/TABLE>\s*/, <DATA>));
   print map { s|<TABLE (.+?)>|$1|; "$line$_" } @tables;
}

sub DotDot {
   my @wanted;
   while (<DATA>) {
      chomp;
      if (/<TABLE / .. /<\/TABLE>/ ) {
         if (/<TABLE (.+?)>/) {
            push(@wanted,$1);
         } elsif (/<\/TABLE>/) {
            print $line, map {"$_\n"} @wanted;
            @wanted = ();
         } else {
            push(@wanted,$_);
         }
      }
  }
}

__DATA__
<TABLE name="table1">
FieldName1 VARCHAR(20)
FieldName2 INT(20)
FieldName3 BOOL
</TABLE>
<TABLE name="table"2>
FieldName1 VARCHAR(20)
FieldName2 INT(20)
FieldName3 BOOL
</TABLE>
[download]