Abstract: In this paper,the elastic semi-infinite space is Considered to be a semi-infinite cylinder,taking into account of the shear stress of this cylinder,in order to simplify the semi-space system.According to the dynamics model of material testing,a calculation formula for foundation vibralion of wave stress damping theory is derived.In some special case,the results are fully in accordance with those of Dr. Yama hara,Dr.Yama hara considered only one-dem-ension wave stiess damping,in this paper both longitudinal wave and transverse wave are taken into cosideration and so the more accurate results are reached. Some discussions are also made in this paper on the inappropriate pointsof the formula given by Dr. Yama hara.