Abstract: The physical and mathematical bases of the elastoplastic framework for constitutive modeling of soils are reviewed. Most of the contents are extracted from the existing literatures, but this paper represents an effort of presenting them in a focused manner, aided with explanatory comments. The review starts from the classical thermodynamic laws and the common hypothesis of internal variables, followed by the elastic-plastic decomposition of deformation and the notion of dissipation and locked energy. Then the concepts of the flow potential and the hypothesis of the maximum dissipation rate as well as the notions of yielding function, flow direction and plastic hardening are elucidated. The pressure sensitive elastic modeling is also discussed. Following the conceptual derivation of the basic ingredients of elastoplastic modeling, the issues on objectivity, anisotropic modeling, non-coaxial deformation and the critical state theory are addressed from a perspective of elementary physics and mathematics.