A new method of analyzing the tapping motion of a cantilever, on the tip of which impulsive force and moment are given, is proposed based on elastic vibration theory. In this method the contact object is assumed to be a spring of which stiffness is hard enough. The force which is given by the spring is regarded as the impulsive force. The product of this force by the gap length between the surface of cantilever and that of the contact object is regarded as the impulsive moment. Contact damping and air damping are also considered. It is newly proved that the modal functions, which satisfy the boundary condition, are not orthogonal in the state that the tip is contact with the object. Taking account of that, the method which solves the initial value problem by using a matrix operation is proposed. By joining the solution in the free state and that in the contact state so as to satisfy the initial conditions at every beginning and ending time of the contact successively, the behavior of the tapping vibration of the cantilever can be analyzed. A micro cantilever, which is assumed to be used for a probe memory head, is adopted as a numerical example, and the motion of it is analyzed by the proposed method. FEM analysis and experiments using a macro scale model are also carried out, and the validity and the merit of saving the calculating time of the proposed method are proved.