The multi-layer ceramic/metal gradient cylinder model is useful for many cnginceringcanses. The heat transfer in the cylinder with coating inside is calculated by analytical method andfinite clement method. The thcrmal stress in a single layer gradient cylinder suffering, eventemperature and a multi-layer gladient cylinder with coating inside suffering uneven temperature isrespectively analzed finite difference method, finite element method and zonced-uniform method.The results show that finite clement method agrees well With analytical method in thc heat transferanalysis; finite difference method, Iinitc clement method and zoned-uniform method agrcc well witheach Other in the thermal stress analysis.