The purpose of this paper is to present a method of material design for the weight reduction, the high thermal radiation and the relaxation of in-plane thermal stress and centrifugal stress in a rotating disk without hole composed of functionally graded material (FGM) with arbitrary thermal and mechanical nonhomogeneities in the radial direction. The disk is subjected to an intermittent heating in an annular region near the outer radius and has an arbitrary variation of heat-transfer coefficient along the radial position on the upper and lower surfaces. The transient temperature field is analyzed by modifying Vodicka's method for onedimensional boundary value problems in composite regions, and the thermal stress and centrifugal stress are respectively obtained by solving approximately the equilibrium equations expressed in terms of the displacement component as Euler's differential equations. The material design is carried out for the rotating disks composed of Ti+6Al+4V and SUS410 FGM, and Ti+6Al+4V, PSZ and SUS410 FGM.