φThe circular tunnel is a common structure in civil engineering. Mohr-Coulomb strength theory has been used to analyses pressure tunnel in the field of rock engineering for many years. Because it could only solve the problems with one kind of material, the application of the theory was greatly restricted. In this paper, the formulas calculating yield range and stresses are deduced based on the proper choice of the first principal stress used in the unified strength theory according to loads and in-situ stresses. The applicability formulas is gained based on the critical pressures, which can be obtained in other situations or strength thoeries simplified by assuming the parameter value in the formula. An example is analyzed, and the yield range versus the inner pressure and stress distribution are presented. Results are compared to those based on the traditional method and significant disparity is observed. The results indicate that the coefficient b, cohesion c, friction angle φ all have significant influences on the yield range and stresses.