In geological media, the solid material and the fluid(s) residing and flowing in its pore space interact with each other, giving rise to hydro-mechanical coupling, which is central to many natural geological processes (e.g., seismic slip) and subsurface engineering applications (e.g., energy recovery and storage, geological storage of waste). This interaction is yet to be better understood, especially when the media deform inelastically and fail by fracturing or slip, or when a multi-fluid system is involved. To this end, we develop a micromechanical numerical model at the grain scale. This model couples mechanics of the solid grains and pore network fluid flow (including single-phase and immiscible two-phase flows). Pore fluid exerts pressure force onto the grains, the motion of which is solved using the discrete element method (DEM). Pore pressure distribution and its evolution are solved via an implicit scheme. For immiscible two-phase flow, effects of capillary entry pressure and viscous pressure drop for the pore throats is currently considered. The pore network is updated regularly in response to deformation of the solid matrix. We discuss the application of the model to studies of fault slip behavior under the influence of pore pressure and studies of fracturing patterns in unconsolidated grain packs.