The nanotechnology based on epitaxial systems includes single or arranged misfit di slocations. In general, whatever is the type of dislocation or the geometry of the array formed by the dislocations; it is important for experimental studies to know exactly the stress distribution for which there is no analytical expression [1,2]. This work, using a numerical analysis, deals with relaxation of epitaxial layers having at their interface a periodic network of edge misfit dislocations. The stress distribution is estimated by using isotropic elasticity. The results show that the thickness of the two sheets is a crucial parameter in the stress distributions and then in the profile of the two sheets. A comparative study between the case of single dislocation and the case of parallel network shows that the layers relaxed better when the interface is covered by a parallel arrangement of misfit. Consequently, a single dislocation at the interface produces an important stress field which can be reduced by inserting a parallel network of dislocations with suitable periodicity.