This short communication identifies some inconsistencies in the numerical predictions of three advanced soil constitutive models. The chosen constitutive models are subject to simple numerical tests in the small strain range relevant to the cyclic response of soil in seismic, offshore and urban applications. The numerical tests comprise: a cyclic simple shear test in the small strain range, a simple shear test with very small strain unloading-reloading loops, and a test on the dependence of the rate of the shear stiffness degradation with increasing shear strain on changing mean confining stress.The results are briefly discussed and, in some cases, the reasons for the observed inconsistencies and potential improvements in the formulations of the investigated constitutive models are initially drafted.