Equations are developed for analyzing the effects of thermal creep on stress distributions. In formulating these elastoplastic equations, the tensile test stress-strain creep data are extended to compound stresses by means of the Mises-Hencky hypothesis. The various equations are manipulated to yield a numerical procedure by means of which the stress and strain components are computed successively at the end of various time intervals. In these calculations it is assumed that the initial creep rates remain constant during each time interval. The resulting equations are applied to the axially symmetric problem of relief of thermal stresses in an infinitely long cylinder which is quickly heated to a parabolic temperature, and maintained at that temperature. End effects are neglected. The calculation is reduced to repeated solutions of a certain second-order ordinary differential equation. Curves are plotted showing the gradual relief of the stresses caused by the creep. The methods developed are illustrative of a procedure which may be followed for other stress-creep problems.