Based on the analytical solutions of a spherical pressure vessel subjected to internal pressure, it points out that the results of membrane stress and bending stress are inaccurate obtained by the one-dimension integral along a line called assessment line in the direction of shell thickness recommended by some references and standards. Therefore, a more accurate method is presented in which the resorted stresses are obtained through two-dimension integral over a ring cross-section area called assessment area of the shell. As an example, an analysis based on the elastic analytical solutions of a thick-walled spherical shell bearing internal pressure shows that the method suggested by this paper can make analysis and design of pressure vessels more accurate.