Excavation of a spherical cavity in an infinite isotropic rock mass subject to a hydrostatic stress field can be regarded as an axisymmetric problem. In order to analyze and evaluate the stability of the excavation of 3D spherical cavity, by invoking the finite difference approximation of the equilibrium and compatibility equations, the distributions of displacement and stress in the potential plastic zone which is divided into a series of spherical shell can be obtained from the outmost shell for which the boundary is known to innermost of the spherical cavity in a successive manner. Linear strain-softening behavior is taken into account, and linear Mohr-Coulomb(H-C) criterion and nonlinear Hoek-Brown(H-B) yield criterion are employed respectively in the procedure. With the increment of the number of the spherical shell, a convergent numerical solution is gotten, and the presented procedure is validated through case studies. On the basis of it, a set of strength parameters which obey cohesion weakening and frictional strengthening law(CWFS model) is studied and the corresponding solution is analyzed. Comparisons of the results from CWFS model and the normal strain-softening model are made and the results from CWFS model seem more reasonable.