Abstarct: Cylindrical cortexes are of the most frequent and significant types of structures found in surrounding environment. Generally, cortexes are limber material usually considered as the most mature structure for their quality in behavior and resistance against the loading and twist. Functional graded material (FGM) gained the significant attention of scientist for their high strength against the high temperature gradient and mechanical loading as well as decreasing the stress concentration on solid material. Hence, the aim of this study is to investigate and modeling the associated stress and displacement of thick wall heterogeneous cylinder under compound mechanical and thermal loading. This study was carried out in four different statuses. - In the first, obtained results of compression loading have lonely studied for the thick wall cylinder using elasticity theory. Governing equation in this state had three possible roots: real, imaginary and binary. Comparison of the numerical modeling results with that of the analytical shows that there is an acceptable agreement between the outcomes of these two methods. - In the second status, thermal loading condition has been analysis using elasticity theory for giving more information about this condition. Obtained results implied that overlaying concept governs the whole condition. In addition, if the associated results of stress analysis, compression and thermal displacements has summed together, stress analysis and displacement of thermo-elastic condition will be obtained. - In the third, compression and rotation loading condition was analysis on the thick wall cylinder using elasticity theory. Solving the governing equation results in finding that sum theory is completely true in this condition either. - Lastly, compression, rotation and thermal loading condition applied on the thick wall cylinder and elasticity theory used for dealing with the outcomes. Regarding to what we have reached, sum theory comes true in this condition as same as the others.