Abstract: The state space theory was introduced and a difference scheme in time domain was applied to establish the state equation of solid cylinder for the analysis of transient heat conduction. In order to check the effectiveness of the present approach, an exact solution for a given initial temperature distribution was provided and the results were compared with that of the present method. The numerical results illustrate that the present approach has high solving precision and is very effective for the transient analysis of heat conducting process of cylindrical shell. Furthermore, the present method can be extended to the analysis of transient coupling thermal stress of composite laminated cylindrical shell.