Thermal cracking under a transient-temperature field in a ceramic/metal functionally graded plate is discussed When the functionally graded plate is cooled from high-temperature, curved or straight crack paths often occur on the ceramic surface. It is shown that the crack paths are influenced by the compositional profile of the functionally graded plate. Transient-thermal stresses are treated as a linear quasi-static thermoelastic problem for a plane strain state. The crack paths are obtained using finite element method with Mode I and Mode II stress intensity factors.