The elastic problem of thick-walled tubes of a functionally graded material(FGM) under internal pressure in the case of plane strain (ε_z=0) has been studied. The model components of the FGM are based on the combination of a matrix with three kinds of elastic moduli of 35, 70, and 210 GPa, and a particle with an elastic modulus of 360 GPa. The distribution profile is assumed by the expressions reported previously for a corundum/ plaster FGM. The elastic stress and strain distributions for the FGM became complicated because of radial elastic modulus gradations. The effects of distribution profiles on the deformation can be summarized by considering the variation of the normalized elastic modulus rate [(dE/dr)/E] in the radial direction. If a greater positive normalized elastic modulus rate is obtained, the circumferential stress at an inner plane of a tube is decreased, and then the tube begins to function as a compound tube.