Abstarct: Prevent structural failure as a result of stress concentration at the geometric discontinuities is one of the important issues in the design of engineering structures. Due to the different parameters on the stress distribution around the cutout of isotropic and composite perforated plates are affected, the correct choice of these parameters will enable designers to achieve optimal plan. In this study, a simple analytical method for stress analysis of perforated plates is presented. The Lekhnitiskii’s solution for circular and elliptical cutout is expanded to polygonal cutout shape using complex variable mapping. In this Thesis, try to study the effect of various parameters consist of: cutout bluntness, rotation angle of hole, fiber angle, cutout elongation, material property alone and then the effect of all parameters together and finally the optimal values of the parameters which leads to less stress concentration will be introduced for any kind of polygonal hole. By comparing different polygonal hole, optimal hole will be introduced. The finite element method has been used to check the accuracy of analytical results. The analytical results are in good agreement with the numerical results. The results indicated, The hole geometry and fibr angle in composite plates can be a significant influence on stress distribution around hole.