Molecular dynamics simulations of Pd clusters supported on the undefective alpha -Al2O3 (0001) surface are reported. The alumina surface is represented by a slab obtained by imposing periodic boundary conditions to a 4 x 4 x 2 supercell. The dynamics of the system is accounted for through classical pair potentials describing both the metal-metal and the metal-surface interactions and have been derived from periodic density functional theory model calculations. Deposited particles show a well defined structure and can be described as truncated pyramids mainly exhibiting (111) facets in agreement with recent scanning tunnel microscopy experiments conducted under atomic resolution. These particles show stability at moderate temperatures (up to similar to 400 K), but when the system is heated (T = 500 K), Pd atoms leave the surface and diffuse into the bulk. Such a diffusion would be in agreement with the loose of activity observed in Pd/Al2O3/NiAl(110) catalysts when the temperature is raised beyond 500 K.