Abstarct: In this thesis, with the development of the classical Lekhnitskii’s complex variable methods, stress resultants analysis of functionally graded plate with elliptical cutout has been studied. By using the complex variable method, Lekhnitiskii obtained the stress resultants distribution around a circular and elliptical hole in anisotropic plates. With the extension of this method to functionally graded Infinite plate and by using the conformal mapping, have tried to investigate the stress distribution around elliptical cutout. For this purpose, the exponential function is used to plate investigated. For modeling the functionally graded plate, the plate is for an asymmetric laminates with gradual change of the fiber directions. In this thesis, the effect of various parameters such as, aspect ratio of cutout shape and hole orientation on force and moment resultants around the hole is considered. FG plate is subjected to uniaxial tention loading. For numerical evaluation ABAQUS software is used to verify the results of the analytical solution. Analytical results are in good agreement with the finite element solution. baxsed on the analytical results. Unexpectedly circular hole is not the best geometry to reduce the stress concentration in perforated plates and in some cases by selecting the aspect ratio of cutout shape and orientation for holes, the stress concentration less than circular hole can be achieved.