Pressure vessels have been in wide use for many years in chemical, petroleum, military industries as well as in nuclear power plants. They are usually subjected to high pressures and temperatures which may be constant or cycling. This paper studies finite element analysis of a spherical pressure vessel under simultaneous thermal and pressure loadings in transient state along with numeric analytical method. A new numeric-analytical method for calculating the transient stress and displacement is introduced. Since the FEM is used for determination of temperature distribution, stress and displacement, therefore, existence of some errors is possible, but because the length and volume size of elements and step time are selected small enough, so, the obtained results are very accurate. Since, the Riemann's integral method is used for calculation of displacement and stress; the created error will be slightly higher. So, by considering the approximate methods used in temperature and displacement calculations and the FEM used in temperature distribution computation, appearance of such errors seems to be normal, thus, if the elements are chosen relatively smaller and much precise methods are used, the errors would be negligible