Abstract: The paper characterizes the fault zone as an idealized interface with linear slip-weakening friction and investigates reflection and transmission of stress wave across two elastic half-spaces on the condition that the initial stress state of rock interface is taken into account. On this basis, the conditions of initial slip and unstable slip are revealed, and the occurrence of dynamic triggering is analyzed which depends on the balance between the incident wave and intrinsic mechanics of fault. The example shows that when the angle of incidence is given, the higher the frequency is, the larger the needed amplitude is.