The slope stability analysis is studied with the nonlinear failure criterion based on the plastic upper limit theorem. The tangent method is assumed to analyse the upper limit solution along the different brusted surface of slope in order to infere the stability coefficient formulas with the nonlinear failure criterion. The initial-tangent method is proposed for the complex slope with logarithmic spiral crack surface; and it can calculate the plastic analysis upper limit solution well. A classical slope calculation case shows that the presented method is of correctness and high precision which agrees well with previous achievements. The new method can be used to guide the slope stability analysis with the nonlinear failure criterion based on the plastic upper limit theorem.