Abstarct: In this thesis has been tried to consider the effective parameters on the stress distribution around of regular polygon cutout in the infinite isotropic and orthotropic plates with particle swarm algorithm (PSO) introduced the optimum parameters to achieve the least amount of stress around the cutout. Design variables include the geometry of cutout, bluntness, rotation angle of cutout, fiber angle, load angle and material properties in orthotropic plates. The finite element method has been used to verify the accuracy of analytical results. Comparison of two methods demonstrates the accuracy of present analytical solution. In this study has been used from analytical method for calculating of the stress components around of various cutout. According to this method using conformal mapping, the development of Lekhnitskii method that was just for the circular and elliptical cutout was used the other cutouts. The results presented in this case shows that by selecting appropriate form of cutout and choice of optimal parameters of the isotropic and orthotropic plates can be significantly reduced stress concentration factor in the plate with cutout and even achieved to less stress concentration factor from stress concentration caused by a circular cutout. In other words contrary to expectations, with the circular cutout is not the best geometry for reduction of stress concentration and in some cases by selecting bluntness, rotation angle and suitable fiber angle for a plate with cutout can be less stress concentration compared with a circularly cutout.