Thermal shock strengths of a plate of a functionally graded material (FGM) are analyzed when the plate is suddenly exposed to an environmental medium of different temperature. A finite element/mode superposition method is proposed to solve the time-dependent temperature field. The admissible temperature, jump that the material can sustain is studied using the stress-based and fracture mechanics-based criteria. The critical parameters governing the level of the transient thermal stress in the medium are identified. The strength of FGMs under transient thermal stresses is analyzed using both maximum local tensile stress and maximum stress intensity factor criteria.