Dynamics　of　the　widespread　saturated　and　semi-saturated　soil-rock　mixtures　(SRMs)　are　of　importance　in　practical　engineering.　In　this　paper,　a　numerical　manifold　model　is　presented　for　hydro-mechanical　simulation　of　the　saturated　and　semi-saturated　SRMs.　In　the　case　of　the　semi-saturated　SRMs,　the　model　is　based　on　the　generalized　Biot　theory　involving　immiscible　two-phase　wetting　and　non-wetting　fluids　in　deformable　porous　media.　The　wetting,　non-wetting　fluid　pressure　and　skeleton　displacement　are　chosen　to　be　primary　variables　which　are　related　to　the　wetting　and　non-wetting　saturation　and　permeability　by　experimental　relationships.　For　the　mechanical　problem,　the　material　interfaces　between　soil　and　rock　are　deemed　discontinuous　by　imposing　a　stick-slip　contact　constraint　using　an　augmented　Lagrange　multiplier　approach.　For　the　hydraulic　problem,　the　material　interfaces　are　continuous　for　the　fluid　pressure　and　flux　fields.　Within　the　framework　of　the　numerical　manifold　method　(NMM),　the　discretized　model　including　the　interfacial　discontinuities　always　can　be　established　using　the　triangular　mesh　and　the　lumped　mass　representation　is　always　available　to　increase　computational　efficiency.　Besides　the　benchmark　problems　of　saturated　and　semi-saturated　porous　media,　two　examples　of　soil-rock　foundation　and　slope　are　performed　to　demonstrate　the　versatility　and　robustness　of　the　model　and　to　investigate　the　hydro-mechanical　responses　of　the　porous　SRMs.　(C)　2020　Elsevier　B.V.　All　rights　reserved.