By　taking　account　of　the　actions　of　the　whole　three　principal　shear　stresses　acting　on　the　dodecahedron　element,　a　triple-shear　yield　criterion　for　materials　was　proposed.　This　criterion　gives　a　unified　yield　expression　to　describe　the　several　common　used　criteria　such　as　the　Tresca　yield　criterion,　the　Von　Mises　yield　criterion　and　the　Mohr-Coulomb　failure　criterion,　through　changing　its　intermediate　principal　stress　effect　parameter　b.　In　spite　of　that,　problems　of　the　limit　inner　pressures　for　the　perfect　elasto-plastic　thin　and　thick　wall　cylinders　and　the　thick　wall　spherical　shells　were　analyzed　and　the　new　unified　solutions　were　deduced.　The　old　solutions　based　on　the　Tresca　yield　criterion,　the　Von　Mises　yield　criterion　and　the　Mohr-Coulomb　failure　criterion　were　only　the　special　cases.　Detail　analyses　on　the　new　solutions　show　that　both　the　intermediate　principal　stress　effect　parameter　b　and　the　tensile/compressive　yield　limit　ratio　a　have　influences　on　the　limit　pressures　for　the　thin　wall　and　thick　wall　cylinders.　But　for　the　thick　wall　spherical　shells,　only　the　ratio　a　has.