This research presents the study on mechanical buckling of thick-walled cylindrical shell made of functionally graded materials with ring supported under uniform axial and lateral loads. The mechanical properties of shell are variable along the thickness direction. First the governing equations on the buckling of the FGM cylindrical shell supported with ring are established based on third-order shear deformation theory. Then the governing characteristic equations were employed, using energy method and by applying the Ritz technique. In the following with solving characteristic equations, the critical load buckling of the FGM thick-walled cylindrical shell supported with axial and lateral loads are calculated. The boundary conditions represented by end conditions of the FGM shell are the following: clamped-clamped and free-free. To verify the validity of the proposed analytical method the results of this research are compared with the results came from using the finite element software. Finally, the effects of the different parameters such as thickness variations, boundary conditions, loading conditions and geometrical parameters of shell and ring on the buckling behavior of FGM thick-walled cylindrical shell are investigated. The results showed that by increasing the FGM volume fraction power in the shell structure, the critical buckling load increases and the location of the ring support has the significant effect on the critical buckling load. The results presented can be used as an important benchmark for researchers to validate their numerical and analytical methods.