Elastic analysis has been used to estimate the driving force for interface edge-crack growth in TBC system with layered FGM coat under an uniform change in temperature. According to some simplified assumptions, closed-form solutions of thermal stresses are obtained and the energy release rates are estimated. For the case of layered FGM, the energy release rate is a function of the geometry parameters of the layers and thermo-mechanical properties of each layer. In addition, the FGM coating system is designed for the purpose of minimizing the energy release rate.