The　Mohr-Coulomb　yield　criterion　takes　on　the　simplest　form　in　the　Mohr　stress　space,　which　has　thus　been　most　extensively　applied　in　limit　analysis　and　limit　equilibrium　methods　because　of　its　accuracy.　However,　the　Mohr-Coulomb　yield　surface　in　the　stress　space　is　non-smooth,　causing　huge　troubles　to　the　constitutive　integration　in　the　deformation　based　finite　element　plasticity　analysis.　In　addressing　strength　problems,　meanwhile,　solvers　based　on　the　load　controlled　method　(LCM)　are　hard　to　bring　the　finite　element　model　to　the　limit　equilibrium　state.　Aiming　at　these　issues,　the　solution　schemes　are　proposed　as　follows.　First,　an　algorithm　named　GSPC　is　designed　for　the　constitutive　integration　for　plasticity　with　non-smooth　yield　surfaces.　GSPC　is　always　convergent　for　arbitrary　large　strain　increments,　with　far　more　excellent　numerical　properties　than　the　return-mapping　methods　available.　A　solver　based　on　the　displacement　controlled　method　(DCM)　is　developed　for　the　finite　element　plasticity　analysis.　The　DCM　solver　is　able　to　bring　easily　the　finite　element　model　into　the　limit　equilibrium　state,　with　no　convergence　issue,　and　far　more　efficient　and　robust　than　any　LCM　solvers.　At　last,　combined　with　the　strength　reduction　method,　the　secant　method　for　the　factor　of　safety　of　slopes　is　developed,　and　the　location　and　depth　of　tension　cracks　at　the　slope　top　are　proposed.　©　2021,　Science　Press.　All　right　reserved.