Taking into consideration the influence of intermediate principal stress on deep-buried circular tunnels, and under plane strain hypothesis, the unified strength criterion was precisely matched to the Drucker-Prager strength criterion. The analytical expression of intermediate principal stress in plastic state for the perfect elastoplastic material with dilatancy was derived from the Drucker-Prager strength criterion. Combining the analytical expression of intermediate principal stress and non-associated flow rule, unified solutions for stress and strain of the tunnel plastic area were obtained. The result shows that the classic solutions of Kastner are special cases of the unified solutions. A practical engineering instance was given according to the unified solutions and the regularities which intermediate and dilation angle act on the surrounding rock of the deepburied circular tunnel plastic area were discussed.