Abstract: The linear relation between shear strength and normal stress of failure plane shows the essential property of soil shear strength. The Mohr-Coulomb criterion, Drucker-Prager yield criterion and Matsuoka-Nakai criterion respectively respond to the linear relationship between shear stress and normal stress on different shear failure planes including shear failure plane with the angle of 45°+φ/2 relating to the plane of the main principal stress, the octahedral plane in the principal stress space of soil element and the spatially mobilized plane named also σ^1/2 spatially mobilized plane. In this paper, new σ^1/3 spatially mobilized plane is proposed using three points κσ₁^1/3, κσ₂^1/3, κσ₃^1/3 in the soil element in the principal stress axes, named as the σ^1/3 spatially mobilized plane. Furthermore, the new strength criterion is also proposed using the shear stress ratio on theσ^1/3spatial mobilization plane being constant. The strength failure surface depicted in the principal stress space by this criterion is a smooth cone surface with the curved triangle shape on plane. The strength failure surfaces of Mohr-Coulomb criterion, Drucker-Prager yield criterion, Matsuoka-Nakai criterion, Lade-Duncan criterion and σ^1/3 spatially mobilized plane criterion described in the stress space as well as the change laws of Lade-Duncan criterion and σ^1/3 spatially mobilized plane criterion with parameter b on different π planes are comparatively analyzed. It is shown that the Lade-Duncan criterion and σ^1/3 spatially mobilized plane strength criterion are approximate, which reveals the physical essence of Lade-Duncan strength criterion, that is, the former approximately obeys the linear relationship between shear stress and normal stress onσ^1/3 spatially mobilized plane at failure of soils. The