The multi-layer ceramic/metal gradient cylinder model is useful for many engineering cases. The heat transfer in the cylinder with coating inside is calculated by analytical method and finite element method. The thermal stress in a single layer gradient cylinder suffering even temperature and a multi-layer gradient cylinder with coating inside suffering uneven temperature is respectively analyzed by finite difference method, finite element method and zoned-uniform method. The results show that finite element method agrees well with analytical method in the heat transfer analysis; finite difference method, finite element method and zoned-uniform method agree well with each other in the thermal stress analysis.