Abstarct: In this study, the analysis of free and forced vibrations of thick-walled cylinders with constant thickness made of porous materials in axisymmetric under mechanical-thermal loading is presented. To derive the equations of motion, the displacement field is estimated using the first-order shear deformation theory that considers the effect of transverse normal strain. The governing equations of the problem as well as the relations related to the boundary conditions are determined using Hamilton's principle, under external pressure and uniform heat flux, which includes a system of differential equations with partial derivatives with constant coefficients. By conducting a case study, the results related to natural frequencies, mode shapes, and forced vibration response were extracted, and in order to validate the results of the analytical solution, numerical modeling of the desired cylinder was also presented and the results of the two methods were compared with each other. The comparison of analytical and numerical results indicates the accuracy of the solution method. In this study, the effect of porosity parameters, temperature changes and geometrical conditions on the natural frequencies and forced response of the cylinder in question has been analyzed analytically and numerically. The results show that the porosity in the thick-walled cylindrical shell reduces the natural frequencies, and the average changes of the radial displacement of the thick-walled cylindrical shell in the homogeneous state is greater than in the porous state.In the final chapter, conclusions and final summaries are made and suggestions are also presented.