Abstract: Based on the limit equilibrium theory of rigid body,a mathematical model for static and dynamic reliabili-ty analysis of abutment stability against sliding is developed in this paper.According to the model calculating formu-las are given in total probability.Furthermore,a practical program is made and used in an example of arch dams.The static and dynamic reliability analysis of abutment stability is discussed in detail and some useful results are ob-tained.It shows that the calculating method presented in the paper is reasonable and can be widely used in the relia-bility analysis of abutment stability against sliding.