In the last years many research works were focused on adhesion in micro-electro-mechanical systems (MEMS). In fact, that phenomenon can endanger the reliability of MEMS, both during the fabrication phase and in the operation conditions. The aim of the present study is to simulate the adhesion phenomena in different environmental conditions, by using Finite Element (FE) computational simulations on a representative part of the surface. A significant part of the work is devoted to the proper generation of FE model for artificial rough surfaces. The micro-scale analyses include the contact behavior of the asperities and the mechanical deformation of the bulk material, which is modeled as elastic-plastic. Some numerical results are presented and compared to previously published data.