Abstarct: The continuous changes of the mechanical and thermal properties of functionally graded materials lead to elimination of the residual stress and effect of the stress concentration, which make increase the strength of this material. 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 stress distribution around the circular hole in finite FG plate, by using the complex potential functions method. The plate subjected to constant uniaxial or biaxial stress; In addition, the boundary of hole is subjected to uniform pressure loading. One of the most important goal of this research is to study the effect of compression stress 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, with specific convergence radius, 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 inhomogeneous 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.