The　corners　of　non-smooth　yield　surfaces,　e.g.,　Mohr-Coulomb　or　Hoek-Brown　criteria,　often　cause　problems　in　numerical　applications　due　to　the　gradient　discontinuities,　which　boil　down　to　the　abrupt　order　interchange　of　two　principal　stresses.　Nevertheless,　when　the　stress　components　cross　the　corners,　the　principal　stresses,　which　are　smoothly　dependent　on　the　components　of　stress　tensor,　can　be　smoothly　tracked　through　subspace　tracking　method.　Thus,　all　the　six　auxiliary　yield　functions　based　on　Koiter＇s　rule　will　be　smooth　functions　of　components　of　stress.　Finally,　the　corner　problems　are　eliminated.　As　an　application,　three　boundary-value　problems　(a　3D　one-element,　a　2D　slope　with　a　soft　band,　and　a　3D　soil　slope)　are　analyzed　to　investigate　the　performance　of　the　proposed　method　in　a　non-linear　finite　element　simulation.