A　two-scale　computational　homogenization　model　is　presented　for　modeling　three-dimensional　(3D)　heterogeneous　poro-elastic　media　in　the　framework　of　the　Numerical　Manifold　Method　(NMM).　The　micro-dynamics　is　fully　incorporated　using　the　extended　first-order　Hill-Mandel　principle　for　simulation　of　the　hydro-dynamic　response.　The　micro　-and　macro-scale　Initial　Boundary-Value　Problems　(IBVPs)　are　simultaneously　solved　with　the　NMM　by　exchanging　quantities　between　different　scales.　The　micro-scale　IBVPs　are　solved　under　both　Linear　Boundary　Conditions　(LBCs)　and　Periodic　Boundary　Conditions　(PBCs).　The　macro-scale　IBVP　is　solved　using　the　Newton＇s　algorithm　iteratively.　For　both　micro-scale　LBCs　and　PBCs,　highly　efficient　algorithms　for　extracting　macro-scale　quanti-ties　and　Jacobian　matrix　from　the　micro-scale　are　established　merely　by　simple　matrix　manipulations　of　the　micro-scale　Jacobian　matrix　without　solving　any　IBVPs.　By　conduct-ing　benchmark　simulations　of　the　heterogeneous　porous　media　under　uniform,　partial　and　impact　loads,　the　accuracy,　stability　and　versatility　of　the　presented　multiscale　model　are　verified.(c)　2022　Elsevier　Inc.　All　rights　reserved.