With　the　construction　of　supertall　buildings　such　as　high　earth　dams,　the　linear　envelope　of　the　Mohr-Coulomb　(M-C)　failure　criterion　fitted　to　lower　confined　pressure　would　significantly　underestimate　the　loading　capacity　of　foundations,　causing　a　huge　increase　in　the　amount　of　earthwork.　Given　that　the　M-C　criterion　has　dominated　in　the　stability　analysis　of　geotechnical　structures,　it　is　proposed　in　this　study　that　the　M-C　criterion　remain　invariant　in　form　but　the　cohesion　c　and　the　frictional　factor　f　be　related　to　the　coefficient　of　intermediate　principal　stress　b,　called　the　Generalized　Mohr-Coulomb　(GMC)　criterion.　In　other　words,　c　and　f　are　both　functions　of　b,　written　as　c(b)　and　f(b).　In　the　simplest　way,　the　GMC　criterion　for　soils,　a　true　three-dimensional　failure　criterion,　can　be　established　by　using　a　piece　of　conventional　triaxial　apparatus.　The　GMC　has　a　non-smooth　strength　surface　like　its　conventional　version.　However,　we　prove　from　true　triaxial　tests　and　the　characteristic　theory　of　stress　tensors　that　the　failure　surfaces　in　the　stress　space　should　be　non-smooth　per　se　for　b　=　0　or　1.　Comparisons　with　other　prominent　failure　criteria　indicate　that　the　GMC　fits　the　test　data　best.