Molecular dynamics simulation was used to study the strain relaxation and evolution of Ag/Cu(111) and Au/Cu(111) heteroepitaxial systems with embedded atom method. By comparing the evolution behaviors of the two systems, the atomistic mechanism leading to the formation of Moir structure in Ag/Cu(111) epitaxial layer is studied and is related to the physical properties of the components in the heteroepitaxial system. It is found that the adhesion between epilayer and substrate is one of the important factors that affect the formation of Moir structure. Positive solution heat of the alloy enables the adhesion of heteroepitaxial system to be weak and is helpful for the formation of Moir structure. The relaxing ability of atoms in epilayer is also important in the formation of Moir structure, which can be related to the bulk modulus of epilayer. The larger the bulk modulus of epilayer, the easier the formation of Moir structure. On the other hand, the formation of Moir structure is related to the island size, which is caused by the boundary atoms confining the relaxation of interior atoms in the island.