Abstract: Based on the theory of stress wave in soil,the radiation damping which is caused in soil of dynamic soil-foundation within the range of the depth of influence,and the fundamental formula of damping ratio of the elastic halfspace by the analog group shear wave velocity are presented in this paper.The analyzed results correspond better with the engineering practice than that of the classical theory of halfspace.The effect of the differential strata in halfspace on the damping is analyzed by theory of wave scattering,and the practical calculation method is presented.On the basis of the theory of wave,the formula of depth affected by the foundation vibration are involved in this study.Finally,taking some engineering project as examples,the results of theoretic calculation and the field observation have been found to be in good agreement.