The use of Rayleigh-Ritz and modified Rayleigh-Ritz techniques for quasistatic thermal stress analysis of nonhomogeneous anistropic elastic bodies is examined. General expressions for the thermoelastic energies are written, and reduction of the general formulation to the problem of a nonhomogeneous orthotropic circular cylinder under a radial temperature distribution is illustrated. Approximate solutions for the deformations and stresses are compared with exact thermoelastic solutions in special cases of homogeneous cylinders, and with finite element solutions in cases of nonhomogeneous cylinders.