Three constitutive models constructed within the spirit of critical state soil mechanics are summarised and compared under conditions of axial symmetry. The models have been calibrated using drained and undrained triaxial compression tests on Hostun sand. The quality of the individual simulations is strongly influenced by the shape chosen for the critical state line at high stresses. Stress response envelopes have been produced in order to contrast the incremental stiffnesses that the models predict for stress and strain paths other than those used for simulation. Plots of second-order work have also been presented for each model. Negative second-order work for certain strain paths indicates the potential for instability and bifurcation of response. Non-associated flow is a basic feature of these models and potentially unstable states were found to occur at mobilised friction angles lower than the peak of the stress-strain response. The hardening moduli of the models are similar, even though they were developed from different starting assumptions.