This　study　first　reviews　the　numerical　manifold　method　(NMM)　which　possesses　some　advantages　over　the　traditional　limit　equilibrium　methods　(LEMs)　in　calculating　the　factors　of　safety　(F-s)　of　the　slopes.　Then,　with　regard　to　a　trial　slip　surface　(TSS),　associated　stress　fields　reproduced　by　NMM　as　well　as　the　enhanced　limit　equilibrium　method　are　combined　to　compute　F-s.　In　order　to　search　for　the　potential　critical　slip　surface　(CSS),　the　MAX-MIN　ant　colony　optimization　algorithm　(MMACOA),　one　of　the　best　performing　algorithms　for　some　optimization　problems,　is　adopted.　Procedures　to　obtain　F-s　in　conjunction　with　the　potential　CSS　are　described.　Finally,　the　proposed　numerical　model　and　traditional　methods　are　compared　with　stability　analysis　of　three　typical　slopes.　The　numerical　results　show　that　F-s　and　CSSs　of　the　slopes　can　be　accurately　calculated　with　the　proposed　model.　(C)　2020　Institute　of　Rock　and　Soil　Mechanics,　Chinese　Academy　of　Sciences.　Production　and　hosting　by　Elsevier　B.V.