The failure of anti-slide pile in earthquake is one important factor that aggravates the harm of mountain hazards. However, the mechanism of it and its response mechanism to seismic wave are not clear at present, and the interaction mechanism between anchor system and seismic wave can’t be resoluted. Therefore, based on energy theory, taking the upper bound theorem used in limit analysis as measure, and assuming the sliding face as arc, the safety of anchor system was defined, and then the mechanism of energy input and dissipation under earthquake was studied. Furthermore, the characters seismic wave which induces the damage of anchor system was also analyzed, and the calculating formulas were suggested. At last, an example was given to show that the failure mechanism of anti slide pile is the result of discontinuous damage accumulation under seismic load with special direction and value.