The bejavior of a bubble near a rigid structure was considered by using the local surface fitting method and the “jet prediction” method. The convergence difficulty caused by the abnormality of the elements was overcome. The flow was numerically simulated by using the boundary-integral method on the assumption that the water was inviscid and incompressible, and the bubble gas obeyed the isoentropic rule. The evolution of the bubble was investigated by means of the mixed Euler-Lagrange method, and the Runge-Kutta method. The important behavior of the bubble, such as migration and jetting, was analyzed in several examples. And the solution of one period of the explosion bubble was obtained. The bejavior of a bubble near a rigid structure was considered by using the local surface fitting method and the “jet prediction” method. The convergence difficulty caused by the abnormality of the elements was overcome. The flow was numerically simulated by using the boundary -integral method on the assumption that the water was inviscid and incompressible, and the bubble gas obeyed the isoentropic rule. The evolution of the bubble was investigated by means of the mixed Euler-Lagrange method, and the Runge-Kutta method. The important behavior of the bubble, such as migration and jetting, was analyzed in several examples. And the solution of one period of the explosion bubble was obtained.