Thermoelasticity behavior of functionally graded thick hollow cylinders with power law and exponentially variations of material properties versus radius is studied analytically. Temperature, displacement and thermomechanical stress distributions are obtained and discussed. Approximate homogeneous multilayer semi-analytical method is used successfully with adequate accuracy and finite layers. Different combinations of ceramics and metals are checked out for thermoelastic stresses due to high temperature and internal pressure. We conclude that the approximate method is simple and has appropriate results. The effects of high temperature on the stresses are more important than the high internal pressure.
