AbstractThe shape of the failure locus of a material is significant for its strength predictions. Even when constitutive models include the same critical stress surface, different critical stress ratios can be predicted for an identical applied isochoric strain path. In this article, we investigate critical stress predictions of different constitutive models, which include the surface according to Matsuoka–Nakai (MN). We perform analytical investigations, true triaxial test simulations with hypoplasticity and barodesy, and discrete element modelling (DEM) simulations to investigate the friction dependency of the stress Lode angle. Our results demonstrate that in hypoplasticity, the direction of the deviatoric stress state at critical state depends solely on the direction of the applied deviatoric strain path. In contrast, in barodesy, the predictions are also dependent on the friction angle of the material. In addition, we compare these results with those obtained with a standard elastoplastic MN model. To validate this friction dependency on the stress Lode angle, we conduct DEM simulations. The DEM results qualitatively support the predictions of barodesy and suggest that a higher friction results in a higher Lode angle at critical stress state.