•A 3D first-order NMM-based multiscale scheme is presented for hydro-mechanics of the heterogeneous porous media.•Micro-scale dynamics is fully considered based on the extended Hill-Mandel lemma.•Simple, closed and efficient algorithms are presented for extracting macro-scale quantities and Jacobian. 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 quantities 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 conducting 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.