You need to use a sizer like this

#!/usr/bin/perl --
use strict; use warnings; 
use Wx 0.86 qw(  );
our %panel;

Main( @ARGV );
exit( 0 );
sub Main {
    my $app = Wx::SimpleApp->new;
    my $frame   = Wx::Frame->new( undef, -1,  "Test window", [ 10, 10 
+], [ 400, 600 ], Wx::wxDEFAULT_FRAME_STYLE()|Wx::wxTAB_TRAVERSAL() );

    MakePanels( $frame );

    my $ShowHideButton = Wx::Button->new( $frame, -1, q[Show(first)/Hi
+de(second)] );
    Wx::Event::EVT_BUTTON( $frame, $ShowHideButton, \&ShowHidePanels, 
+);
    
    
    
    $frame->SetSizer( Wx::BoxSizer->new( Wx::wxVERTICAL() ) );
    $frame->GetSizer->Add( $ShowHideButton, 0, Wx::wxEXPAND() );
    $frame->GetSizer->Add( $panel{first},   1, Wx::wxEXPAND() );
    $frame->GetSizer->Add( $panel{second}, 1, Wx::wxEXPAND() );
    
    
    

    $frame->Show(1);
    $app->SetTopWindow($frame);
    $app->MainLoop;
} ## end sub Main

sub MakePanels {
    my( $frame ) = @_;
    $panel{'first'} = Wx::Panel->new( $frame, -1, [ -1, -1 ], [ -1, -1
+ ], );
    $panel{'first'}->SetBackgroundColour( Wx::wxRED() );
    $panel{'first'}->Hide();
    Wx::StaticText->new( $panel{'first'}, -1, 'First panel', );
    
    $panel{'second'} = Wx::Panel->new( $frame, -1, [ -1, -1 ], [ -1, -
+1 ], );
    $panel{'second'}->Show();
    $panel{'second'}->SetBackgroundColour( Wx::wxBLUE()  );
    Wx::StaticText->new( $panel{'second'}, -1, 'Second panel' );
    
    return;
} ## end sub MakePanels

sub ShowHidePanels {
    my ( $frame, $event ) = @_;
    my $button = $event->GetEventObject;
    my $label  = $button->GetLabel();
    if ( $label eq 'Show(first)/Hide(second)' ) {
        $label = 'Hide(first)/Show(second)';
        $panel{first}->Show();
        $panel{second}->Hide();
        $frame->GetSizer->Layout(); ##!!!!
    } else {
        $label = 'Show(first)/Hide(second)';
        $panel{first}->Hide();
        $panel{second}->Show();
        $frame->GetSizer->Layout(); ##!!!!
    }
    $button->SetLabel($label);
} ## end sub ShowHidePanels
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