Abstract: This paper presents a new integral equation for 2D and 3Dthermal stress analysis of structures consisting of functionally gradedmaterials. Using this equation together with the three-step multi-domain BEMtechnique, thermal stress analysis can be carried out for complicatedstructures comprised of arbitrarily many numbers of media with varyingmaterial properties. The Kelvin fundamental solutions independent of elasticmodulus are used in this paper. As a result, the resulting integralequations include domain integrals due to the non-homogeneity andtemperature variations of the material. All these domain integrals aretransformed into equivalent boundary integrals using the radial integrationmethod (RIM), resulting in a pure boundary element analysis algorithm.Finally, two numerical examples are given on 2D and 3D thermal stressanalysis of two typical thermal protection systems for space shuttles toverify the correctness of the proposed formulation by comparingcomputational results with those obtained by the finite element method.