To　investigate　the　two-phase　seepage–stress　coupling　process　in　fractured　porous　medium,　this　study　extends　the　cohesive　element-based　numerical　manifold　method　(Co-NMM)　by　incorporating　a　two-phase　seepage–stress　coupling　model　considering　the　effect　of　matrix-fracture　interface　on　the　two-phase　flow　and　fracture　propagation　induced　by　the　two-phase　seepage　pressure.　The　proposed　two-phase　flow　solving　framework　implicitly　calculates　the　fluid　pressure　and　saturation　of　the　two-phase　flow　based　on　a　two-phase　unified　pipe　network　method.　Furthermore,　to　more　realistically　model　the　hydraulic　behaviour　of　two-phase　flow　in　fractured　porous　medium,　a　matrix-fracture　interface　condition　called　the　extended　capillary　pressure　condition　is　incorporated　into　the　two-phase　flow　solving　framework　to　capture　the　interactions　among　fluid　flow　in　the　fractures　and　matrix.　Due　to　the　inheritance　of　the　Co-NMM,　one　key　advantage　of　the　extended　method　is　the　simulation　of　complex　multi-fracture　propagation　caused　by　the　two-phase　seepage–stress　coupling.　The　two-phase　flow　solving　framework　is　first　validated　by　reproducing　the　water　displacing　oil　in　a　single　fracture　and　the　gas　displacing　water　in　a　single-fractured　porous　medium　against　analytical　and　numerical　solutions,　respectively.　The　two-phase　seepage–stress　coupling　procedure　is　then　verified　by　performing　a　one-dimensional　consolidation　problem　of　soil　column,　in　which　comparisons　between　the　numerical　and　analytical　results　regarding　the　pore　pressure　and　compression　displacement　are　presented.　Finally,　with　the　extended　method,　CO2-enhanced　oil　recovery　in　fractured　reservoir　is　preliminarily　studied　by　considering　the　effect　of　gas　injection　rate　and　capillary　pressure　on　the　evolution　of　two-phase　flow　and　fracture　propagation.　The　results　elucidate　that　high　CO2　injection　rate　can　lead　to　fracture　propagation　in　the　reservoir,　and　both　capillary　pressure　and　fractures　have　a　significant　effect　on　the　CO2　distribution.　©　2021　Elsevier　B.V.