You can purchase and download a limited selection of "PS2 Classics" directly from the PlayStation Store. These digital versions are designed to work on any PS3 model.
If you have a or Super Slim , you cannot play PS2 game discs. However, you still have options: Can You Ps2 Games On Ps3
Compatible models have 4 USB ports on the front. If your console only has 2 USB ports, it is not officially backward compatible with PS2 discs. You can purchase and download a limited selection