One-dimensional transient and residual stress fields in a hollow cylinder of functionally graded materials (FGMs) for two models of ceramic-metal systems are studied subjected to severe thermal shock. It is clear that residual stresses in FGMs arise primarily from spatial variations in the thermal expansion coefficient, but can be significantly modulated by the Young's modulus gradient. Analytical results of the thermal stress required to reduce the transient stress and residual stress in the FGM provide a means of appropriate microstructure design for FGMs to select FGM constituents and spatial variation in material properties.