Abstract: Based on mathematical calculations,failure criteria of Lade-Duncan,modified Lade-Duncan and Matsuoka-Nakai could be transformed into J 2 = g(θ σ)? f(I1),and the corresponding ridge function g(θ σ)was derived from these failure criteria.It was proved that these failure criteria shared common ridge function g(θ σ)and there were intrinsic relationships among failure criteria of Lade-Duncan,modified Lade-Duncan,Matsuoka-Nakai and Ottosen in spite of their completely different mathematical expressions.Finally,according to the true triaxial test results of concrete and clay,these failure criteria were verified and some important conclusions were obtained.