The new failure criterion of J₁·J₂/J₃=const. which has been proposed on the basis of the "spatially mobilized plane (SMP)" is introduced as a failure criterion for granular materials (J₁, J₂ and J₃ : the first, second and third effective stress invariants). This failure criterion is called the Matsuoka-Nakai ("SMP") criterion. The Tresca and Mises criteria are usually adopted as failure criteria for metals, and the Mohr-Coulomb and Matsuoka-Nakai criteria for granular materials such as soils. The Matsuoka-Nakai criterion has a concept of averaging the Mohr-Coulomb criterion, in such a way that the Mises criterion has a concept of averaging the Tresca criterion. Such interesting relationship among the Tresca, Mises, Mohr-Coulomb and Matsuoka-Nakai criteria is discussed by reviewing their physical meaning, their forms of equations and their shapes in three-dimensional stress space.