The study of thermal stresses on pressure vessels has a great significance from the theoretical and practical point of view due to their importance in many applications. This paper presents a complete analysis of thermal stresses within a thick-walled cylinder under dynamic internal temperature gradient. A complete evaluation of temperature and stress distributions, in a non-steady state, is obtained using a numerical model. In this model the temperature of the inside surface of the thick-walled cylinder is considered to change according to certain boundary conditions. The harmonic and periodic loading conditions are also studied.