There are several models of the PlayStation 3, and not all of them are capable of playing PS2 games. Here are the models that can play PS2 games:

• CECHA01: 60GB model with full hardware backwards compatibility.
• CECHB01: 20GB model with full hardware backwards compatibility.
• CECHE01: 80GB model with partial software emulation.

Other models, including the slim and super slim models, are not backwards compatible with PS2 games. However, all PS3 models can play "PS2 Classics" that can be purchased from the PlayStation Store. If you have a modded PS3, you can use it to play any PS2 game, even if your model doesnt normally support it.