In　this　paper,　an　elasto-plastic　dynamic　constitutive　model　for　transversely　isotropic　fluid-saturated　porous　media　is　constructed　based　on　the　SMP　failure　criterion,　and　the　time-domain　explicit　finite　element　method　for　the　wave　propagation　in　transversely　isotropic　elasto-plastic　fluid-saturated　porous　media　is　put　forward.　The　wave　propagation　in　transversely　isotropic　elasto-plastic　fluid-saturated　porous　media　is　investigated　based　on　the　dynamic　constitutive　model　and　the　time-domain　explicit　finite　element　method　given　out　in　this　paper,　and　calculating　results　are　compared　with　those　of　elastic　wave　propagation.　Calculating　results　show　that　the　dynamic　response　of　transversely　isotropic　elasto-plastic　fluid-saturated　porous　media　is　remarkably　different　from　that　of　elastic　porous　media,　that　is　the　peak　value　of　elasto-plastic　dynamic　response　has　remarkable　increase　relative　to　that　of　elastic　dynamic　response,　and　the　figures　of　time　history　are　different　significantly　from　each　other　for　elasto-plastic　dynamic　response　and　elastic　dynamic　response　of　transversely　isotropic　fluid-saturated　porous　media.　In　the　meanwhile,　numerical　calculations　carried　out　in　this　paper　indicate　that　the　time-domain　explicit　finite　element　method　is　effective　for　the　wave　propagation　in　transversely　isotropic　elasto-plastic　fluid-saturated　porous　media.