Abstract: In the light of porous media model developed from mixtures theories, the solid skeleton was considered as elasto-viscoplastic material, and an elasto-viscoplastic model of saturated porous media was established. By adding a time parameter in inviscid elasto-plastic constitutive relation, the viscoplasticity was introduced into the solid skeleton. A penalty finite element formulation was attained by using Galerkin weighted residual method, and a Newmark predictor-corrector iterative scheme was designed to solve the nonlinear finite element system equations of rate-dependent porous media. The scheme is good at calculating the dynamic response of saturated elasto-viscoplastic porous media model. Through two numerical examples, the saturated elasto-viscoplastic porous media exhibited obvious rate-dependent property and time effect. Not only the displacements, solid stresses, plastic zone of solid skeleton, but also the flow velocity, pore pressure of interstitial fluid were presented and discussed.