Abstract: Twin　shear　unified　elasto-plastic　associated　and　non-associated　constitutive　model,　which　is　based　on　the　Twin　Shear　Unified　Strength　Theory　Yu,1991,　is　proposed　in　this　paper.　　The　authors　give　a　classification　of　singularities　and　discusses　their　solutions　of　the　proposed　unified　elasto-plastic　constitutive　model,　which　are　also　applicable　to　singular　yield　surface　such　as　Tresca,　Mohr-Coulomb　and　others.　　This　unified　consitutive　model　has　been　implemented　in　UEPP　(Unified　Elasto-Plastic　finite　element　Program).　　Twin　Shear　Unified　Strength　Theory　(or　　Unified　Strength　Theory),　unified　elastoplastic　constitutive　model　and　UEPP　constitute　a　comprehensive　system　of　elasto-plastic　theoretical　analysis,　finite　element　implementation　and　engineering　application.