This paper numerically and analytically investigates a non-linear static, two-dimensional thermoelastic analysis in the radial and tangential directions of a cylindrical shell made of functionally graded materials. The dependence of material properties on temperature makes the heat governing equations non-linear. To obtain the temperature field analytically, the heat conduction equation is linearized and exactly solved using a linearizing transformation, then this exact solution is substituted in the Lamme-Navier equations, and the elasticity equations are numerically solved using a second-order central finite difference method, and displacement and stress distributions are obtained. Finally, the temperature field, stress, and displacement distributions are presented, and the effect of inhomogeneous parameters on them is examined and discussed. The correctness and accuracy of the exact analytical solution of the temperature field are illustrated by a comparison with the numerical solution. The results show a good agreement.