Is it rigid or flexible? The stiffness of the mat will make a difference. If rigid, the edge bearing pressure will be higher than that at the center. If flexible, the bearing pressure will be the same at all points. Suggest you look at Poulos and Davis' Elastic Solutions for Soil and Rock Mechanics - Chapter 7, here:
I believe that jdonville miss spoke. If rigid the pressure will be the same everywhere. If flexible the pressure will be higher at the location of the applied loads.