Amongst all hydrological and environmental problems the most typical one is ground water contamination. Waste material is to be placed in engineered landfill as ground water contamination can take place due to landfill leachate. In order to design engineered landfill mathematical models proposed for the landfill. The general model of the ground water layer include various hydro geological process as contaminant transport, mechanical dispersion, molecular diffusion, sorption, chemical reactions, etc. the time behaviour of a contaminated ground water layer is to be predicted for practical situation. Realistic data for mathematical model is to be analysed using realistic results. Various soil parameters porosity, dispersivities, sorption, coefficients etc. are to be used in the model. The objective of this study is to develop and validate mathematical model that would address the problem of migration of contaminants from the bottom of landfill. This concentration was found to be in a consonance with the simulated concentration with chloride and sodium in ground water considering one dimensional transport model. Governing equation of contaminant transport involving advection-diffusion using explicit finite difference method with upwind correction.