Abstract: The stress response envelope, a kind of geometric representation for tangential stiffness of constitutive models, is an efficient approach for qualitative studies on characteristic features of the constitutive models. With regard to the typical constitutive models for soils falling in the categories of hypoelasticity, elastoplasticity and hypoplasticity, the Duncan model, the Cam-clay model and the Gudehus-Bauer model are taken as examples for this study. Stress response envelopes are presented with a discussion of the general features of the corresponding constitutive models. Comparisons are made for the characteristics of the models of three types. It is shown that the essential defects exist in the hypoelastic model for modeling soil loading and unloading. For the elastoplastic model, the model response to a change of loading direction at stress points near or on the failure surface is unrealistic. For the hypoplastic model, while the main feature of continuous dependence of the tangential stiffness on the direction of strain increment is expected, difficulty exists in simple formulation for capturing stress paths of soil tests in undrained conditions.