Abstract: Based on the method of lumped-mass explicit finite element and local transmitting artificial boundary, a time domain method is presented for the computation of dynamic stiffness of rigid foundations resting on or embedded in saturated poroelastic soil. The two-phase behavior of porous medium is represented according to Biot's theory. The technique is applied to the computation of dynamic stiffness of rigid plate on a saturated poroelastic half-space. Compliance component are computed and compared with existing results. The effects of properties of porous medium and the embedded depth on the dynamic stiffness are examined. The method presented in this paper is able to represent more general properties and geometries of soil and foundation than the existing approaches do.