The paper presents the solution of the wave equation describing the attenuation of the vibration amplitude in the soil during pile driving. It is suggested that in the soil there is the area around the pile where the energy dissipates due to plastic deformations, and then the areas of the elastic state where surface waves propagate. In the framework of the wave model, the connections have been determined between vertical vibrations of the embedded solid body circular in plane and the motions in the area of the elastic soil state which is described by an integrity of infinitely thin layers. The interaction of the pile and soil in the plastic deformations area is beyond our consideration, though its size is of high importance for the problem solution. The formula has been derived, which permits, having the result of amplitude measurement in any point by a vibrometer and the position of surface wave propagation boundary, evaluating the soil vibrations at different distances from the pile driving point. The quantitative and qualitative agreement of the measured amplitudes and results of analysis obtained during test pile embedment performed during field measurements and found in references proves that the proposed model can be used to increase the accuracy of evaluation of the vertical soil vibrations.