Abstract: Mohr-Coulomb criterion leads to convergence difficulties in the numerical calculation due to the presence of singularity. Firstly, the singularity problem is mainly caused by the principal stress’s nonsmoothness when Lode angle changes, and then the theoretical basis of the principal stress space are given. Mohr-Coulomb criterion’s equivalent complementary model is presented in the principal stress space based on Koiter’s rule, and the Fischer-Burmeister complementarity function is used to describe the model, which makes the Newton algorithm be successfully solved. The proposed algorithm can remove the singularity of the Mohr-Coulomb criterion and avoid the trial process of the conventional methods, and it also improves the accuracy of the Mohr-Coulomb criterion. Examples verify the validity and reliability of this method.