Abstarct: In this research thermoelastoplastic analysis of thick-walled cylinders made of homogenous and nonhomogenous materials with power-varying properties using plane elasticity theory which is subjected to internal pressure and steady state thermal loading is carried out. The purpose is to check yielding of cylinder by assuming elastic-perfectly plastic behavior and to find state of stress, strain and displacement of cylinder. First, governing differential equation axisymmetric thick-walled cylinders with constant thickness that are made of homogenous and nonhomogenous materials with power-varying properties and subjected to pressure and thermal loadings are derived by using plane elasticity theory at the plane stress and plane strain condition. Then according to the Tresca yield criterion analytically and von Mises yield criterion numerically by using ABAQUS finite elements software, investigate yielding of cylinder and stress, strain and displacement in elastic and plastic region of cylinder. Finally, for the case study and survey equation, are considered a homogenous and FGM cylinder with the specified parameters.