The　incidence　angle　of　seismic　waves　plays　a　pivotal　role　in　the　stability　analysis　of　structures　in　near-field　zones.　Despite　its　importance,　the　application　of　obliquely　incident　seismic　waves　within　models　of　discontinuous　media　has　been　limited.　This　study　introduces　a　novel　approach　that　integrates　the　oblique　incidence　of　seismic　waves　into　a　coupled　model　employing　both　the　Finite　Difference　Method　(FDM)　and　the　Discrete　Element　Method　(DEM).　We　validate　the　accuracy　of　seismic　wave　propagation　under　oblique　incidence　in　two　FDM-DEM　coupling　models-overlapping　coupling　and　interface　coupling-through　comparisons　with　theoretical　solutions.　For　vertically　incident　seismic　P-waves,　both　models　yield　similar　results.　However,　under　oblique　incidence,　the　overlapping　coupling　model　demonstrates　superior　accuracy,　with　a　maximum　error　of　approximately　4.217　%,　compared　to　about　10　%　in　the　interface　coupling　model.　Our　findings　also　show　that　while　the　relative　sizes　of　particle　diameter　and　overlap　length　minimally　affect　accuracy,　the　arrangement　of　particles　markedly　influences　the　results.　Furthermore,　we　apply　this　method　to　a　slope　model　to　investigate　the　failure　process,　revealing　that　the　nature　of　the　sliding　body　shifts　from　tensile　sliding　to　tensile　ejection　as　the　incidence　angle　increases.