In this report the plastic interaction of asperities sitting on a rough surface is investigated. The plastic interaction between asperities is particularly important for the sliding of two surfaces; it plays a key role in the wearing process. Recent studies show that the transition from low wear to mild wear regime is due to plastic interaction between surface asperities. We aim to study the process at continuum mechanics level; being the problem very complex we will make several simplifications. We model asperities as rigid spheres and we study the indentation of an elastic-plastic half plane for normal and tangential load. Moreover we prescribe the stress profile induce by the contact at the surface interface; we assume a Hertzian stress profile. All the simulation are performed using Finite Element Method.