Reasonable choice of rock strength criteria is crucial for stress and displacement prediction and support design in tunnel engineering. Based on Mogi-Coulomb strength criterion and elastic-perfectly plastic model, analytical solutions of stress and displacement for surrounding rocks around a circular tunnel were derived The intermediate principal stress coefficient was used to present the intermediate principal stress effect. The results in this study were compared with the current solutions in the literatures and the influence of intermediate principal stress and shear strength parameters of surrounding rocks was discussed. The results showed extensive applicability and the Mohr-Coulomb strength criterion and Matsuoka-Nakai criterion are two special cases; when the intermediate principal stress coefficient b was equals to 0.5, the results indicated that the intermediate principal stress effect and its range for rock strength; the influence of cohesion and internal friction angle on the plastic radius and tunnel wall displacement was significant; Care should be taken to the effects of intermediate principal stress and shear strength parameter variations of surrounding rocks on tunnel design and construction.