Thermal stress problems of a functionally gradient plate as one of the advanced high-temperature materials capable of withstanding the extreme temperature environments, with and without an edge crack, are discussed One of the most important problems of the thermal stress in the functionally gradient plate with the crack are how to decrease the thermal stress intensity factor and how to determine the optimally continuous profile of the composition of the plate. The functionally gradient plate is subjected to a cycle of heating and cooling on the ceramics surface of the plate. The material properties of the functionally gradient plate are dependent on the temperature and the position. The optimally continuous profile of the composition of the plate is discussed. The numerical results for thermal stresses and the thermal stress intensity factor are shown for many temperature conditions and for many continuous profiles of the composition of the plate.