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. In this paper, is tried to present the analytical solution to calculate the stress distribution around the circular hole in infinite FG plate, by using the complex potential functions method. The plate is subjected to thermal and mechanical loads; which is in-plane stress at boundary edges, a uniform pressure loading at boundary of hole and a steady thermal loading. The variation of Material properties, especially Young's modulus and thermal expansion coefficient, is in a radial direction and concentric to the hole. One 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. It is observed that FG plate with increasing young modulus has better behavior at radial displacement than FG plate with decreasing young modulus.