Abstract: In slope stability analysis, the efficiency of searching a critical slip surface increases as the degree of freedom of the solution space decreases, but the narrowed solution space may not be able to cover all the potentially true slip surfaces. In contrast, an increase in the degree of freedom by adding new vertexes of the surface curve can expand the solution space but lower searching efficiency, also undesirable for finding the true solution. Therefore, how to generate slip surfaces is a key question in slope stability analysis. Based on reviewing the traditional methods, this paper presents a new measure for generation of slip surfaces using polar coordinates, a logistic function, and parametric equations. And a comprehensive function for slip surfaces is constructed to simplify slip surface fitting. This measure converts the geometric problem of slip surface generation to a problem of determining the parameters of a known function. Thus it would help reduce the degrees of freedom of the slip surface spaces and narrow the searching ranges of the parameters.