In geotechnical engineering, boundary value problems are often idealized under plane strain conditions. It is therefore of particular interest to investigate constitutive models with respect to plane strain failure. In this contribution, previous studies on elastoplastiticity are linked to the here presented studies on hypoplasticity and barodesy. The parameters of the models are chosen in such way that strength predictions coincide for drained axisymmetric triaxial conditions. The plane strain strength predictions differ due to different failure surfaces and due to different deviatoric directions of stress paths under plane strain conditions. The influence of the initial stress state on peak strength is discussed. As barodesy and hypoplasticity are formulated within the asymptotic state concept, critical stress states are independent of the initial stress state. The results of element test observations are related to a strength reduction analysis.