Limit equilibrium analysis method is used to estimate slope stability in common. And abundant experience has been accumulated in long time practice. However

a weakness of limit equilibrium method is that uncertainties of parameters and models can not be considered. And its application would be influenced in practice. Uncertain and correlative problems in slope system can be solved effectively by reliability theory. But the partial derivative of performance function is hard to be calculated. The reliability analysis method is inconvenient to be applied in practice. So as to solve the deficiency

a numerical computational method based on dual function approximation is developed. In a rectangle area

an incomplete dual quadratic polynomial which is constructed by Lagrange method is used to approximate the performance function. Then its partial derivative can be calculated approximately; and the mean and deviation can also be obtained. So the reliability index and failure probability can be calculated by the first-order second-moment method. Mabaoying landslide in Enshi region of Hubei province is used to be a case study. It shows that the results with first-order second-moment method based on dual function approximation is consistent with the results by the push method and Monte-Carlo method; and it can be satisfied the engineering requirements in practice.