There are several weak structural planes in some gravity dams with complex foundation, which will affect the anti-sliding stability of deep layer. In order to explore the problem, we establish a finite element model of gravity dam-foundation system for a reservoir project by using finite element software of ANSYS. We adopt a comprehensive method of overload and strength reduction, considering water load and the change of material factor at the same time. Then, in association with cusp catastrophe theory, we obtain the variations of horizontal displacement at feature points and relative displacement between upper and lower points of weak interlayer with comprehensive coefficient. By establishing the standard potential function of the model, we can judge that gravity dam is instable or stable according to the function’s discriminant. In order to represent structure state better, we should adopt proper index such as the relative displacement between upper and lower points of weak structural plane. Anti-sliding stability coefficient of the example is within the range of [3.125,3.188] by using the comprehensive method, while in traditional rigid limit equilibrium method, the range is [3.039,3.667], so the two ranges are similar. For more precise identification of instability, we should combine criteria mentioned with other criteria and develop a comprehensive evaluation system.