In　this　paper,　two-dimensional　ordinary　state-based　peridynamic　(OSB-PD)　plastic　model　is　coupled　mechanically　with　the　Drucker-Prager　(D-P)　criterion,　aiming　at　numerically　reproducing　localized　deformation　and　locating　the　critical　failure　surface　of　slopes.　A　non-physical　(or　negative)　incremental　plastic　energy　can　be　avoided　under　extreme　non-uniform　deformation　in　this　model.　The　strength　reduction　method　is　adopted　to　estimate　the　critical　failure　surface　and　factor　of　safety.　For　PD　strength　reduction　method,　three　evaluation　criteria　are　introduced　to　estimate　the　critical　damage　state　of　slopes.　Two　numerical　simulations　including　a　classical　slope　model　and　centrifuge　tests　of　sand　slopes　are　performed　by　the　proposed　PD　method.　The　critical　failure　surfaces　of　slopes　are　obtained　by　PD　and　compared　with　the　results　obtained　by　(i)　the　finite　element　method　(FEM),　(ii)　the　simplified　Bishop　method,　and　(iii)　the　centrifuge　tests.　The　numerical,　analytical　and　experimental　results　have　collectively　verified　the　proposed　PD　method.　©　2022　Elsevier　Ltd