While all PlayStation 3 consoles can play original PlayStation discs, not all PS3 models are PS2-compatible. If you want to play PS2 games on your PS3, you'll need to make sure you buy the right model.
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The original 60GB and 20GB launch models are backwards compatible with PS2 games because they have PS2 chips. Other models, notably the 80GB Metal Gear Solid PS3, used emulation software to be backwards compatible, but no longer support PS2 games. Here's how to tell if your PS2 is backwards compatible:
How to tell if your PS3 is a PlayStation 3 Slim Model. You can tell if a PS3 is a slim model if it has a lower profile, a matte black finish (not glossy), and the PS3 logo on the top instead of the word "PlayStation 3." If it is a PS3 Slim, it is not PS2 backwards compatible, but you can still play PS1 games on it.
Check if the PS3 is a 20GB PlayStation 3. These were only available at launch. Here’s what to look for: