Because of the continuous changes of mechanical properties of functionally graded materials and therefore reducing the effects of stress concentration, many researchers are interested in studying the behavior and use of these materials in various industries. For the correct design of perforated inhomogeneous plate is needed to know the accurate information about the deformation and stress distribution in different points of the plate especially around the hole. In this paper, is tried to present the analytical solution to calculate the 2D stress distribution around the circular hole in long FG plate, by using the complex potential functions method. The plate subjected to constant uniaxial or biaxial stress. One of the most important goal of this research is to study the effect of compression load applied to the hole boundary on stress distribution around the hole. The variation of material properties, especially Young's modulus is in a radial direction and concentric to the hole. The special exponential function is used to describe the variation of mechanical properties. The finite element method has been used to check the accuracy of analytical results for homogeneous and heterogeneous plates, also for all loading cases. In the presence of applied load at the boundary of circular hole, amount of radial stress in addition to hoop stress is considerable. Therefore the Von Mises stress is used to study the stress around the hole. The results showed that inhomogeneous plate with increased modulus of elasticity has greater load bearing capacity with respect to homogeneous plate.