Abstract: It is assumed that the failure of geomaterials is determined by stress ratio between shear stress and normal stress on the characteristic surface based on its friction behavior. The concept of effective stress ratio is proposed and it is expressed by the ratio between shear stress and normal stress on characteristic surface. The stress ratio on characteristic surface can be expressed as the tangent value of straight line deducted by the intercept circumscribing the mohr's circle in σ-τ coordinates in two-dimensional condition. It is assumed that there is a three-dimensional physical space plane in XYZ space considering every two adjacent physical coordinate plane under three-dimensional space. The shear stress ratio on characteristic surface in three-dimensional space is the determinant factor influencing the failure behavior of material and the proposed criterion can be signed as a criterion. SMP (spatially mobilized plane) criterion and generalized Mises criterion are two special cases of the a criterion. When the value of intercept in two-coordinates is zero, the proposed criterion is degenerated to SMP criterion. When the value of tangent is zero, the proposed criterion is degenerated to generalized Mises criterion. When the intercept and angle of circumscribing line are not zero, the proposed criterion in deviatoric plane is between the above those. The curved triangular form is exhibited between the curves of SMP criterion and generalized Mises criterion in deviatoric plane. A coupling of compression and shear behavior yield criterion is adopted and a power function is adopted as failure criterion. A shape function is proposed based on the proposed criterion in deviatoric plane. The criterion expressed by p and q is substituted by the proposed criterion expressed by three dimensional stresses and the transformation stress equations are deduced based on proposed criterion. In general a constitutive model expressed by p and q can be converted as a three-dimensional model simply. Through yield and strength behaviors and a variety of stress paths test contrast, the rationality of the proposed criterion and transformation method are verified.