This paper contains the exact and general solutions for the thermal stress in a semi-infinite solid and a thick plate under steady distribution of temperature. The approach used rests on the method of Hankel transforms in the three dimensional theory of elasticity which is introduced into the axisymmetric case by Harding and Sneddon and generalized to the unsymmetric case by the present author. It is found that the stresses in the direction normal to the plane surface, that is, σz, тθz and тzr vanish everywhere in a semi-infinite solid and a plate with infinite extent when the distribution of temperature is steady. The general solution is then used to solve some particular problems of a thick plate. Numerical calculation is carried out in detail and the result is compared with the corresponding solution for a thin plate.