This study investigates a prediction model for free-field response in the vicinity of a vibrant foundation. The model is based on a mathematical description of physical phenomena that occur when the massless machine foundation system is charged. This constitutes a source of a harmonic vertical force. The foundation has a square and rigid shape and is assumed to be placed on the surface of viscoelastic soil overlying bedrock. Vertical displacements of both the foundation and the surrounding soil are obtained by solving the wave’s equation while considering the conditions of the dynamic soil foundation interaction. The solution of this equation is formulated in the frequency domain Boundary Element Method. In this work, the Thin Layer Method is used to calculate the Green’s functions for each element. By this approach, the amplitudes of the soil in the vicinity of a vibrant foundation may be obtained under the effect of various parameters.