The effects of the composition gradient in the radial direction on thermal stress have been analyzed for thick-walled tubes of functionally gradient material (FGM) under uniform thermal loading. The combinations of aluminum and silicon carbide were assumed to be the same as the plaster/corundum model. The distributions of the stress and strain components depended mainly on the composition gradient. Its qualitative estimation seems to make it possible to consider the variations in the linear expansion coefficient and elastic modulus. The circumferential stress at the inner surface varied from tension to compression according to the increase in composition gradient accompanied by a decrease in the linear expansion coefficient and an increase in the elastic modulus. For generalized plane strain conditions (axial strain, εz=constant ≠0), circumferential stress and radial stress are independent of axial strain. The optimum composition gradient generated by compressive circumferential stress at the inner surface is estimated.