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Evolutionary polynomial regression (EPR) is a novel soft computing technique, which has been developed recently, and was initially used for modeling environmental phenomena by its presenters. Later on, other activities such as evaluating uplift capacity of suction caissons, shear strength of reinforced concrete deep beams, predicting superficial foundation subsidence, and determining the liquefaction potential of sands have been conducted by EPR technique. In this paper, the results of some experiments on municipal waste materials of Tehran are used to develop a new EPR-based model to predict the stress-strain behaviour of municipal waste material buried in Kahrizak landfill. The experiments were focused on the effects of shearing rates, and vertical stresses. The results of afterward statistical analyses showed the robustness of the new predictive model.