A method to estimate the radiatio power to the surrounding formation due to axial vibration of the pipe in a fluid-filled borehole has been developed, by using the propagation modes of stress wave in an infinitely-long and uniform drilling borehole surrounded by a radially-infinite homogeneous formation. Also, the equivalent damping coefficient for the axial vibration of the pipe has been derived. As an example, results for a real drilling borehole has been presented. The analysis of the elastic motion of the infinite formation which has cylidrical cavity is simplified with the geometric axisymmetry and the low-frequency assumption so that the analytic solution is obtained.