A　three-dimensional　(3D)　numerical　manifold　formulation　with　continuous　nodal　gradients　(H8-CNS)　is　presented　for　dynamic　analysis　of　saturated　elasto-plastic　porous　media　based　on　the　three-variable　(u　-　w　-　p)　formulation.　Using　meshes　of　8-node　hexahedra　as　mathematical　patches,　the　skeleton　displacement　(u)　and　fluid　velocity　(w)　interpolations　are　constructed　with　a　constrained　and　ortho-normalized　least-squares　(CO-LS)　scheme　and　a　piecewise　constant　interpolation　for　fluid　pressure　field　is　employed.　One　feature　of　H8-CNS　is　to　overcome　locking　in　both　limiting　cases　of　low　permeability　and　rigid　skeleton.　Another　feature　of　H8-CNS　is　to　achieve　higher　accuracy　in　stress　results　for　porous　media　problems　involving　both　elastic　and　elasto-plastic　skeleton　behaviors.　H8-CNS　is　also　able　to　fully　capture　dynamic　responses　of　porous　media　under　high-frequency　loading.　The　accuracy　and　stability　of　H8-CNS　are　verified　by　performing　a　variety　of　numerical　simulations.　Time　integration　of　H8-CNS　is　shown　to　be　stable　and　accurate　using　the　energy　balance　condition.　(C)　2021　Elsevier　B.V.　All　rights　reserved.