Since　the　stability　of　a　landslide　is　mainly　controlled　by　the　strength　properties　of　the　slip　band　rather　than　the　sliding　body,　naturally　the　boundary　element　method　is　an　excellent　tool　for　the　stability　analysis　of　the　landslide,　where　the　slip　surface　is　regarded　as　a　contact　boundary　between　the　sliding　body　and　the　slip　bed.　By　casting　the　contact　problem　into　a　mixed　variational　inequality　problem　(MiVIP),　the　convergence　in　dealing　with　contact　nonlinearity　has　been　proved　significantly　improved.　In　this　study,　the　strength　reduction　technique　is　applied　to　bring　the　slope　to　the　limit　equilibrium　state.　A　so-called　critical　element　on　the　slip　surface　is　always　fixed　to　maintain　the　convergence　during　the　strength　reduction.　Based　on　the　fact　that　the　strength　redundancy　of　the　critical　element　vanishes　at　the　limit　equilibrium　state,　the　method　of　bisection　is　designed　to　find　out　the　factor　of　safety.　A　typical　example　and　an　engineering　bank　slope　are　analyzed　to　demonstrate　the　numerical　properties　of　the　proposed　procedure.