SINGH M proposed a nonlinear Mohr-Coulomb (M-C) criterion by adding a correction term to the original M-C criterion which could only linearly express rock strength variation with confining pressure. The nonlinear M-C criterion assumes that there is a critical state when the confining pressure reaches the uniaxial compressive strength of rock material, however it has a large discrepancy with some triaxial experimental results. In order to expand the application of the nonlinear M-C criterion, a general expression of M-C criterion is developed by further improving the correction term. A comparison among the general expression of M-C criterion, the nonlinear M-C criterion and the hyperbolic model is made by using triaxial data of 11 different kinds of rock. Analytical results show that the M-C criterion with the modified expression has a higher accuracy than the other two criteria. The strength values predicted by the generalized M-C criterion is consistent well with experimental values. Thus, the generalized M-C criterion has wider application than the nonlinear M-C criterion.