Weak structural surface is one of the key factors controlling the stability of slopes.The stability of rock slopes is in general concerned with set of discontinuities.However,in soft rocks,failure can occur along surfaces approaching to a circular failure surface.To better understand the position of potential sliding surface,a new method called simplex-finite stochastic tracking method is proposed.This method basically divides sliding surface into two parts:one is described by smooth curve obtained by random searching,the other one is polyline formed by the weak structural surface.Single or multiple sliding surfaces can be considered,and consequently several types of combined sliding surfaces can be simulated.The paper will adopt the arc-polyline to simulate potential sliding surface and analyze the searching process of sliding surface.Accordingly,software for slope stability analysis using this method was developed and applied in real cases.The results show that,using simplex-finite stochastic tracking method,it is possible to locate the position of a potential sliding surface in the slope. Weak structural surface is one of the key factors controlling the stability of slopes.The stability of rock slopes is in general concerned with with of discontinuities. However, in soft rocks, failure can occur along surfaces approaching to a circular failure surface. To better understand the position of potential sliding surface, a new method called simplex-finite stochastic tracking method is proposed. This method basically divides sliding surface into two parts: one is described by smooth curve obtained by random searching, the other one is polyline formed by the weak Structural surface.Single or multiple sliding surfaces can be considered, and several several types of combined sliding surfaces can be simulated. The paper will adopt the arc-polyline to simulate potential sliding surfaces and analyze the searching process of sliding surfaces. Accredited, software for slope stability analysis using this method was developed and applied in real cases.The results show that, using simplex-finite s tochastic tracking method, it is possible to locate the position of a potential sliding surface in the slope.