Abstarct: In this research thermoelastoplastic analysis of thick-walled cylinders made of nonhomogenous materials with power-varying properties using first-order and third-order shear deformation theory which is subjected to internal and external pressure and steady state loading is carried out. The aim is to check yielding of cylinder by assuming elastoplastic (elastic-perfectly plastic) behavior and to find state of stress, strain and radial displacement of cylinder. First differential equations governing axisymmetric thick-walled cylinders with constant thickness that are made of nonhomogenous materials with power-varying properties and subjected to pressure and thermal loadings are derived using shear deformation theory and virtual work principle. Method of solving these equations for cylinder with clamped-clamped and clamped-free ends is expressed. Then the procedure of checking cylinder yield using Rankine, Tresca and von Mises criteria and correction of stress, strain and displacement fields obtained by elastic solution in yielded regions is expressed. Also the solution of same problem using finite element method is expressed in this thesis. Numerical results are presented for a special cylinder and compared with results obtained by solving problem using Abaqus FEM software. Finally a comparison between shear deformation theory and finite element method is made.