We simulated the bubble collapse accompanied by the formation of liquid jet using the Boundary Element Method. We apply the smoothing technique to prevent numerical instability of the surface mesh. The curvature effect is taken into account in the smoothing of the grid points. We compare the present three-dimensional numerical results with the axisymmetric results. It is shown that present numerical results have sufficient agreement with the axisymmetric ones. It is also shown that present method is effective for the simulation of three-dimensional asymmetric bubbles.