Stability reliability analysis of abutment rock of arch dam is a very complicated problem which must be studied and solved. Generally, entirely sliding stability reliability analysis should be made when abutment rock bounded by structure planes like fault, joints and fissures, and layers is possible to slide. Due to the complex causes and structures, diverse litholigy, different rocks have different mechanics attributes. While the physical and mechanical parameters of the same rocks are of obvious dispersion and uncertainty. And it is also complex to calculate the pushing force at arch abutment on dam abutment rock, because the uncertain factors as water pressure, sediment, variable temperatures and materials parameters are contained. In this essay, based on Stochastic Finite Element Method, the formula of sliding stability reliability analysis of dam abutment rock is given. The formula can be used for entirely stability reliability analysis of dam abutment.