In the field of engineering combine incompatible properties such as heat, abrasion and corrosion resistance as well as a tough, capable of machining, and welding capabilities and ect, can have many applications, that these incompatible properties exist in the functional behavior. In this material the volume two of the combinatory gradual change from one to another can. Because their properties such as modulus of elasticity, coefficient of thermal expansion, coefficient of thermal conductivity, coefficient of Poisson, and ... Gradual changes in the internal are affected. Swimming Kith most types of FGM is a combination of metal and a refractory ceramic. Shell or shell structures of the most abundant and most diverse types of structures that are found in the physical world around us. Generally curved shell structures are of the quality of Behaviors and resisting forces and Torque compiled, the top level structures are placed. Proportion to the desirability of behavior, the complexity of their analysis is important. Approximate analytical methods for analysis of shell theory based on assumptions that form the shell. The shells, spherical shells, due to symmetry in geometry, are of particular importance. In this thesis, has been analyzed the analytical and numerical solution for the functionally graded material (FGM) hollow sphere under thermo mechanical loading with linearly increasing boundary temperature. The recent use of spherical shells maid from homogeneous and non homogeneous materials, regarding their extensive application in various industries such as petrochemical industries, defense industry, oil and gas industry and aerospace industry, has been the main motivation in the present study. Particularly, stress analysis of a FGM spherical shell is carried out under a pressure and thermal loading.For this intent, FGM is introduced. Then the literature related to this study, has been reviewed. In the next step, the governing equations, which are the terms of Navier equations, are expressed. The materials properties except Poisson ratio are assumed to be continuously changed in the radial direction. In addition, it is assumed that the inner surface temperature increasing linearly from zero, reaching a peak point of steady state. In the analysis presented here, also the effect of non-homogeneity in FGM thick sphere was implemented by choosing a dimensionless parameter, named n i (i = -2..2), which could be assigned an arbitrary value affecting the stresses in the sphere. For solving the equations, temperature distribution of the transient heat transfer is obtained for homogenous and non homogenous material, taking advantage of Laplace technique and series solving method for ordinary differential equation. Using plane theory of elasticity (PET) are obtained the radial stresses distribution, hoop stresses and radial displacement components for the hollow sphere under internal and external pressure. For validating the results obtain from analytical solution, finite element analysis (FEA) is carried out using commercial software, ABAQUS. As an example, a FGM hollow sphere with material properties follow a power law is calculated, and numerical results are graphically presented. Results show that there is a great agreement between the numerical results obtained from FE simulations and those obtained from the presented analytical solution. Keywords: FGM, Hollow sphere, Thermo mechanical stresses, Finite Element, Linear thermal load