Strain relaxations at metallic interfaces are usually predicted on the basis of macroscopic lattice mismatch. The new concept of mesoscopic mismatch is introduced, which will be more appropriate to discuss stress and strain fields near metallic islands on metallic surfaces. Using recently developed ab initio based many body potentials, the impact of mesoscopic mismatch on heteroepitaxial and homoepitaxial growth is investigated. Co and Cu islands on Cu(1 0 0) and Co islands on Cu(1 1 1) are studied.