The　failure　mechanism　of　slope　instability　is　complex,　and　the　characteristics　of　sliding　surface　often　show　complex　forms　such　as　compression　shear-tension　failure.　Based　on　the　finite　element　strength　reduction　method,　the　limit　stress　field　and　strain　field　of　slope　are　obtained.　Starting　from　the　limit　stress　field　of　three-dimensional　slope,　and　considering　tension-shear　composite　failure,　the　positioning　problem　of　slope　critical　sliding　surface　is　transformed　into　the　initial　value　problem　for　solving　the　first-order　quasilinear　partial　differential　equation,　namely,　the　Cauchy　problem.　The　tensile　failure　mode　is　adopted　in　the　equal　tensile　stress　area　at　the　scarp　of　the　slope,　and　the　shear　failure　mode　of　Mohr-Coulomb　yield　criterion　is　adopted　in　the　passive　sliding　area.　In　this　way,　the　critical　slip　surface　is　determined　without　assuming　the　geometry　of　the　slip　surface　and　specifying　the　slip　mode　automatically.　The　three-dimensional　slope　of　gently　inclined　structural　plane　and　steeply　inclined　structural　plane　are　studied　respectively.　Not　only　the　geometric　characteristics　and　distribution　of　the　two　are　described,　but　also　compared　with　the　jointed　homogeneous　slope.　Finally,　combined　with　the　physical　model　test,　the　failure　characteristics　of　homogeneous　slope　under　uniformly　distributed　load　in　ultimate　stress　state　are　studied　to　verify　the　correctness　and　reliability　of　the　method.　©　2022　Academia　Sinica.　All　rights　reserved.