Based on the upper bound limit analysis theorem and the shear strength reduction technique,the equation for expressing critical limit-equilibrium state was employed to define the safety factor of a given slope and its corresponding critical failure mechanism by means of the kinematical approach of limit analysis theory.The nonlinear shear strength parameters were treated as variable parameters and a kinematically admissible failure mechanism was considered for calculation schemes.The iterative optimization method was adopted to obtain the safety factors.Case study and comparative analysis show that solutions presented here agree with available predictions when nonlinear criterion reduces to linear criterion,and the validity of present method could be illuminated.From the numerical results,it can also be seen that nonlinear parameter m,slope foot gradient β,height of slope H,slope top gradient a and soil bulk density Y have significant effects on the safety factor of the slope.