Abutments of concrete arch dams are usually crossed by several joints which may create some rock wedges. Abutment stability analysis and controlling the probable wedge movements is one of the main concerns in the design procedure of arch dams which should be investigated. For decades, the quasi-static method due to its simple approach is used by most of dam designers. In this study the dynamic method is presented and the obtained time history of sliding safety factors are compared to the quasi-static results. For this purpose, all three components of Kobe 1979 and Imperial Valley 1940 earthquakes are applied to the wedge, simultaneously and the magnitude and direction of wedge displacements are calculated based on Newmark method which is not possible in the quasi-static approach. A 3-D finite element model of Luzzone dam including dam-foundation-reservoir interactions is used to compute the thrust forces. The obtained results indicate that quasi static method is more conservative. The importance of uplift pressure effects on the abutment stability is investigated as well. It is shown that the uplift pressure can play a key role in the abutment stability analysis and it is necessary to control the uplift pressure and seepage in arch dam foundations.