Abstract: To describe the shear yield and failure behavior of soils in the generalized 3D stress space, the critical state constitutive model needs to be combined with some strength criteria. The use of various 3D model generalization approaches is frequently highly important in characterizing the impacts of stress Lode angle and deviatoric stress on stress and strain, especially under plane strain. The unified hardening (UH) constitutive model for K₀ consolidated soils and the spatially mobilized plane (SMP) strength criterion are used as examples, and the transform stress (TS) and g(θ) methods are adopted for the 3D model generalization. The 3D elastoplastic stiffness matrix D_ep associated with each model generalization approach is deduced, and the key difference between various approaches for calculating 3D stress and strain is discussed. The TS method, in comparison to the g(θ) method, is able to transform the yield curve on the π plane from a nearly circular shape under a low stress ratio to the shape of the SMP strength criterion at failure, which demonstrates the consistency from yield to failure. Predictions of a series of plane strain element tests and boundary value problems are performed with the 3D UH model generalized by the TS and g(θ) methods. The results show that the predicted results from the TS method are more consistent with the existing experimental measurements. Due to the irregular shape of the failure surface when using the g(θ) method, the estimated stress level is often either too high or too low under plane strain for K₀-consolidated soils.