The　seismic　response　behavior　of　fluid-saturated　porous　media　(FSPM)　has　been　a　critical　subject　in　the　area　of　soil　dynamics　and　geotechnical　earthquake　engineering.　In　this　paper,　the　numerical　study　of　the　seismic　response　of　the　FSPM　is　performed　based　on　the　u-p　dynamic　formulation.　A　time-stepping　explicit　algorithm　for　the　numerical　solution　to　the　u-p　dynamic　formulation　is　developed.　The　precise　time　integration　method　is　adopted　in　the　algorithm　to　improve　the　computational　accuracy.　The　transmitting　artificial　boundary　is　used　to　describe　the　energy　radiative　effect　of　the　wave　motion　in　the　FSPM.　The　numerical　results　indicate　that　the　time-stepping　explicit　algorithm　developed　in　the　current　study　is　applicable　and　effective　for　the　numerical　solution　of　the　dynamic　problems　of　the　FSPM　based　on　the　u-p　dynamic　formulation.　Furthermore,　parametric　studies　are　performed　to　investigate　the　effect　of　the　permeability　coefficient,　elastic　modulus　of　the　solid　skeleton　and　porosity　on　the　dynamic　response　of　the　FSPM.　The　analyses　show　that　the　permeability　coefficient　value　has　a　negligible　effect　on　the　solid　skeleton　displacement　but　has　a　noticeable　impact　on　the　pore　fluid　pressure.　With　the　decrease　of　the　permeability　coefficient　value,　the　peak　pore　pressure　increases　remarkably.　The　elastic　modulus　of　the　solid　skeleton　has　an　important　effect　on　the　solid　skeleton　displacement　and　pore　fluid　pressure.　With　the　decrease　of　the　magnitude　of　elastic　modulus,　the　solid　skeleton　displacement　and　pore　fluid　pressure　increase　remarkably.　The　porosity　value　has　an　insignificant　effect　on　the　solid　skeleton　displacement　but　has　a　significant　impact　on　the　pore　fluid　pressure.　With　the　increase　of　the　porosity　value,　the　peak　pore　pressure　decreases　significantly.