Frictional interface commonly exist in nature and kinds of materials. The dynamic behavior of the frictional interface has a profound impact on the macro strength and other properties of materials. This paper mainly studies the influence of finite fracture of the micro contact the interface under stress wave loading theoretically and simulatively. Based on the micro contact fracture mechanism of friction, a two-dimensional interface friction model including a triangular micro bulge is established with linear elastic constitutive relationship and D-P failure criterion. The results show that the interaction of the incoming stress disturbance and the micro bulge will induce the fracture of the bulge, and with the decrease of the inclination angle of the micro-contact, the fracture position of the triangular micro contact gradually moves upward from the root, and a crack propagating towards the matrix occurs in the top corner of the triangle. Moreover, in the micro process of fracture, a three wave profile centered on the fracture surface: longitudinal wave, transverse wave and interface wave, will be generated A new interesting phenomenon is that at the moment of loading, a micro stress disturbance is produced synchronously from the interface and propagates to the substrate in the form of longitudinal wave. More comparative examples and analysis show that the mechanism of this disturbance is related to the overall gravity micro adjustment acting on the interface. This work connects fracture and wave, and reveals the finite fracture of micro contact of the friction interface and wave effect, which is expected to provide an effective way for earthquake prediction, so as to advance the earthquake prediction time.