A computation model of circular openings based on nonlinear constitutive relationship along slip lines is introduced. Discontinuous expressions for stress state around the openings after excavation are deduced based on the model. Distributions and values of stresses in surrounding rock are controlled by a uncertain load parameter
which could be determined by introducing a boundary condition. Stress distribution curves of surrounding rock in different ranges of the load parameter are obtained
where the ranges of the load parameter are determined by stress state in surrounding rock. The discontinuous analytical solutions of surrounding rock stress state are consistent with the numerical solutions of two dimensional finite element code for local shear strain.