A theoretical framework to describe the behavior of natural clay is proposed in a new four-dimensional space, consisting of the current stress state, stress history, the current voids ratio, and a measure of the current soil structure. A key assumption of the proposed framework is that both the hardening and the destructuring of natural clay are dependent on plastic volumetric deformation. Two different assumptions about how this destructuring occurs are proposed, based on which two versions of a complete constitutive model have been formulated. The behavior of reconstituted soil can also be simulated by the proposed model as a special case where the structure of soil has no effect on soil deformation. Characteristics of the proposed model are demonstrated through systematic simulations of the influence of soil structure on clay behavior. The simulated behavior of natural clay is compared qualitatively with widely available experimental data. It is seen that the proposed model successfully represents the main features of natural clays with various soil structures.