This paper applies numerical methods to investigate the non-spherical bubble collapse near a rigid boundary. A three-dimensional model, with the mass conservation equation reformulated for considering the compressibility effect, is built to deal with the coupling between the pressure and the flow velocity in the momentum and energy equations and to simulate the temporal evolution of the single bubble oscillation and its surrounding flow structure. The investigations focus on the global bubble patterns and its schlieren contours, as well as the high-speed jet accompanied when the bubble collapses and the counter jet is generated in the rebound stage. The results show that the robust pressure waves emitted due to the bubble collapse lead to substantial changes of the flow structures around the bubble, especially the formation of the counter jet generated in the rebound stage. Furthermore, compared with the high-speed jet when the bubble collapses, the counter jet in the rebound stage emits the momentum several times greater in the magnitude and in diametrically opposite direction at the monitoring point.