This paper concerns a theoretical treatment of three-dimensional coupled thermal stress problems in a cylindrical body having transversely isotropic material properties. The first section of the paper is devoted to resolution of the coupled forms of the temperature field and the associated thermoelastic field into the uncoupled forms by using the modified potential-function method and introducing a perturbation technique. Then, in the next section, we analyze a three-dimensional coupled thermal stress problem of an infinitely long hollow cylinder having transversely isotropic properties. In our analysis we carry out the numerical calculations for several values of the orthotropic parameters of material constants. These effects on the temperature and the associated stress distributions are then examined briefly.