Abstarct: The abundant use of shells in engineering structures has led researchers to focus on analyzing the behavior of these structures under various loading conditions. In this study, using the Plane Elasticity Theory (PET), analytical and numerical solutions of homogeneous and heterogeneous FGM thick wall spheres, are presented under compressive and transient thermal load. The loading involves: internal pressure, external pressure, transient thermal load and also the combination of these loads together. The properties in heterogeneous sphere varying with the power functions in terms of the radius of the sphere, but the Poisson ratio is constant. By applying Fourier's law ,in heat transfer problems, the governing equation (heat transfer equation) has been obtained and solved by using separation of variables and variable change method and respect to the boundary conditions, it becomes an eigen quantity problem and finally, the response functions expanded in terms of eigen functions. The temperature boundary conditions include heat transfer at the inner and outer surfaces of the sphere and the ambient temperature is assumed constant. By applying constitutive, kinematic and equilibrium equations and using Cauchy-Euler method and method of variation parameters, radial displacement is calculated and by using the closed-form solution, radial and circumferential stresses are achieved. The values used in this study are arbitrarily chosen to demonstrate the effect of time and inhomogeneity on the distribution of temperature, displacements and stresses. To check the results accuracy of analytical solution, a finite element solution by modeling in software Abaqus has been used in all cases of loadings for homogeneous and inhomogeneous shell and Good agreement is made between the results of these two methods.