Abstarct: The aim of this study is to investigate and modeling the associated stress and displacement of thick walled heterogeneous cylinder under mechanical and thermal loading. The governing equation of the thick cylinders have been extracted using energy method for exponentially varying properties of material under internal and external pressure, the solution of the final equation has been indicated and by case study, results and graphs of the stress and displacement distribution for different boundary conditions have been indicated. For investigating the accuracy of results conducted from analytical solution, the numerical modeling of cylinder has been done and the results of two methods compare. Also, for elastic analysis of rotary cylindrical shells, by doing general solution of the cylinders under pressure loading, stress and displacement distribution for different B.C has been indicated and the results compared with that of analytical solution. Furthermore, thermo-elastic analysis of the cylindrical shells under pressure and uniform heat flux for different boundary conditions have been conducted and comparing the results with that of numerical shows that FSDT is not efficient on thermo elastic analysis. So for analysis of cylinders under mechanical, rotational and thermal loading, third order shear deformation theory has been used. Comparison of the numerical modeling with that of analytical shows an acceptable agreement between outcomes of these two methods. Finally conclusion, discussion and suggestion have been indicated.