This paper presents an analytical and a numerical thermomechanical investigation of a thick-walled cylinder made of the functionally graded materials (FGMs). The hollow cylinder is subjected to a pressure and a thermal load and the properties of this material are varying across the thickness from the inner face that is a ceramic to the outer one which is a metal. After validating the current results by the analytical results, the thermomechanical behavior of the cylinder in the transient condition is investigated and the hoop and radial stresses and also temperature distribution are reported. The results reveal that the use of FG material causes a decrease in the stress; thus, it significantly improves thermomechanical behavior of the domain, thanks to using FG materials.