Abstarct: Plates and shells are most applicable structures in engineering. Analysis and investing this structures under mechanical and thermal loading is one of most important engineering problems that many scientists are interested in. Different engineering structures such as ships, airplanes, submarines and rockets are always subtended to mechanical and thermal loading in order to their application; Therefor it is necessary to know accurate information about deformation and stress distribution in different points of shell. In this paper, analytical and numerical solution of FG rotating pressurized thick cylindrical shells under transient thermal load is presented under generalized plane strain and plane stress assumptions, respectively using plane elasticity theory. The loading is in the form of thermal, rotational and mechanical at the same time. The material properties are assumed to vary non-linearly in the radial direction, and the Poisson ratio is assumed constant. Temperature distribution assumed to be one dimensional through the radial direction that is obtained using the method of the separation of variables, generalized Bessel functions and eigen function method. The distribution of temperature, radial displacement and thermal stresses are obtained in a transient state for general thermal boundary conditions and through the radial direction of the cylinder and time are plotted. the results are compared with the solution using finite element method (FEM), which showed good agreement. The values used in this study are arbitrarily chosen to demonstrate the effect of inhomogeneity on the distribution of displacements and stresses. To obtain displacement through the radial direction, Cauchy-Euler equation and method of variation of parameters is used to solve equilibrium equation. By substituting displacement function in constitutive equation radial and circumferential stresses are obtained 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 has been used in all cases of loadings for inhomogeneous shell.