In this study, the theoretical analysis of a three-dimensional thermal stress problem is developed for a functionally graded rectangular plate due to a partial heat supply in a transient state. Assuming the functionally graded rectangular plate has nonhomoge neous thermal and mechanical material properties in the thickness direction, the three-dimensional temperature in a transient state and three-dimensional transient thermal stresses in a simple supported plate for functionally graded material are analyzed by introducing the theory of laminated composites as one of theoretical approximation. As an example, numerical calculations are carried out for a functionally graded rectangular plate made of zirconium oxide and titanium alloy. Some numerical results for the temperature change, the displacement, and the stress distributions are shown in figures.