This paper presents conceptual development of fundamental concepts of modelling the elasto-plastic behaviour of expansive soils stabilized soils with lime and cement. The stabilization is accomplished with both lime and cement treatments of expansive soils where lime proves to be the best additive in treatment of plastic soils than cement. The concepts of the yield surfaces of the Tresca, von-Mises, Drucker-Prager, Mohr-Coulomb and Cam-Clay elasto-plasticity models are reviewed. Because the initial consumption of lime (ICL) of 3.5% with the mellowing period of 4 hours was established for the expansive soils, the lime stabilization of 4%, 6%, 8% and 10% of lime by weight of dry soil was added to the soils and cured for 7, 14 and 28 days. Cement contents of 2%, 4% and 6% were used for the cement stabilized specimens. Both treated and untreated soil specimens were tested in the laboratory to determine which model accounts for the complex elastoplastic behaviour of both treated and untreated expansive soils. The treated and untreated specimens were characterized in terms of model performance. Of all the reviewed models, the Modified Egg Cam Clay model was able to decribe reasonably many features of the behavior of both untreated and treated expansive soils. The model is superior because it is characterized with the limited number of constitutive parameters easily determined in the laboratory or even in situ.