Multi-layer Pd(100)/gamma-Al2O3(100) slab models were constructed over a non-defective gamma-Al2O3 (100) surface in order to study the Pd oxidation steps including penetration of atomic oxygen from the surface to Pd bulk. The modeling using periodic DFT/PBE revealed that near the surface both chemisorbed O atoms or physisorbed O-2 can play a promotive role regarding O diffusion starting from c(2x2) model of O adsorption. The calculated activation energies E# for O diffusion from Pd(100) surface approach experimental E# values between the deeper layers while underestimate the rearrangement barriers at the surface. We also calculated the activation energies of CH4 and O-2 dissociation considering different Pd-Pd distances in the Pd and oxidized Pd(O*) layers on different types of oxide support shown earlier.