Many mathematical models developed to predict the stress-strain curve of soil. Most of them are complicated because of the complexity nature of soil material. Moreover, soil behavior is apparently unpredictable due to the fact that every type of soil has its own inherent properties that cannot be represented by a single model. Hence, the objectives of this paper is to review the mathematical models available in the literature and to assess the applicability, limitation and the basic requirement in order to apply the models. Also, this paper will look on the basic principles of the models and the basic characteristic that should have on the models for the best prediction capability. This paper will review the basic models such as th elastic models (Hooke's law and hyperbolic models), simple elastic plastic models (Drucker-Prager, Mohr Coulomb, DiMaggio-Sandler, PLAXIS Soft Soil and Lade and Duncan), Critical State Soil Models (Modified Cam Clay, elasto-viscoplastic, Structured Cam Clay, Anisotropic Cam Clay) and Bounding surface models (Dafalias and MIT-E3). Some weaknesses will also be highlighted to shed some light for further improvements.
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