Seismic dynamic stability analysis of arch dam abutment has been a hot topic in geotechnical engineering. However, studies are not yet mature on the evaluation methods and criteria of dam abutment dynamic stability. The advantage of the finite element method and limit equilibrium method are combined to improve the abutment dynamic stability analysis method. Then the seismic dynamic overload method and limit cumulative displacement criterion are proposed. Firstly, a real-time dynamic analysis is conducted based on the finite element method. Secondly, multi-grid method is adopted to calculate the resistance force and sliding force of abutment potential slip blocks through stress interpolation, it can determine the main sliding direction and calculate the dynamic safety factor using the limit equilibrium method for each slider. Meanwhile, there is an acceleration integral to get the cumulative displacement of slip blocks for the period within which the safety factor is less then 1.0. According to the slider size and the sliding surface strength parameters, the limit cumulative displacement formulation is proposed and acted as the instability criterion of slip blocks; by comparing the cumulative displacement and the limit cumulative displacement, the stability of the slider is determined. An abutment dynamic stability analysis system SAFEDAM is established from the above ideas. To verify the rationality of the limit cumulative displacement criterion, Shapai arch dam is taken as example which has underwent the Wenchuan 5.12 earthquake in Sichuan province. The results show that for the left bank abutment of Shapai arch dam, the overload stability safety factor Kp0 is 3.2, while for the right bank the Kp0 is 4.2. The example study confirms that the proposed method provides a new path for the dynamic stability of arch dam abutment and evaluation. For the reliability and flexibility to assess the dynamic stability analysis, the method shows its wide applicability in engineering practice.