Abstract: In the dynamic finite element analysis of saturated porous media in unbounded space or half-space, a finite region is usually selected for computing ,so how to deal with the boundries of this finite region is the key procedure for stimulating and analysing the open system. Based on Biot's dynamic theory about saturated porous media,the normal and tangent stress formulaes are deduced for cylindrical waves and spherical waves propagating outward in unbounded saturated porous media.According to the formulaes , the viscous-spring dynamical artificial boundary is developed in this paper on which continuely distributing physical components such as viscous damping or parallel connecting spring and viscous damping are placed on the artificial boundaries to stimulate the affection of unbounded media..The exemples show that the viscous-spring dynamical artificial boundaries have fine accuracy and stability.Key word: saturated porous media, Viscous-spring dynamical artificial boundary, wave motion