In this paper, we analyze thermal-stress characteristics of functionally graded materials (FGM), the newly introduced layered composite materials with great potential as next generation composites. Among the several material parameters governing its characteristics, we study the effects of the material variation through the thickness and the size of the FGM layer inserted between metal and ceramic layers using the finite element method. Through a representative model problem, we observe different thermal stress characteristics for different material variations and sizes of FGM. This basic study provides insight into the concept of FGM and lays the foundation of FGM optimization to control thermal stresses.