Abstract: Stability against sliding along the slide plane of concrete gravity dams is closely related to the friction coefficient f and cohesion c of the contact surface. In design criterion of the gravity dams， sometimes f and c are regarded as the constant values, and sometimes regarded as random variables where distribution is specified. In fact，f and c are not constant or don′t accord with a given distribution. For the distribution of the stability safety factor against sliding of the gravity dam, very little research achievements can be found. In this paper， aiming at problems of stability against sliding along the foundation base of the concrete gravity dams， a reliability method is used in the studies of the effect on the stability safety factor K brought by the random distribution linear， the mean values and coefficients of variation of the friction coefficient f and cohesion c， revealing the discrete character and the varying patterns of the probability distribution curves and reliability index. The research results will contribute to the further recognition of the design criterion of the gravity dams.