Instructions
Double-check to make sure what PlayStation 3 version you are running. If it is the newer Slim model, you aren&'t going to have a problem. Additionally, the older PS3 with a 20 or 60 gigabyte memory system allows you to play PS2 games.
Power on the Sony PlayStation 3 and eject any disc currently inside the disc drive.
Insert the PS2 game disc and wait for the hardware to read the disc. A prompt window appears, stating the game is an older PlayStation 2 format.
Click "Yes" to proceed and the PlayStation 3 uploads necessary file updates. This process takes a few minutes. Once complete, the game loads onto the screen, ready for you to play.