The quantitative study of the groundwater contamination in a porous media is a difficult task. For complex problems, numerical solutions are the most effective means to study the movement of contaminants in the groundwater. The solute transport model used in this study has proved to be an efficient tool to model contaminant transport for complex problems. The model demonstrates its effectiveness in reproducing the contamination by chlorides of the roundwater at the landfill site due to leachate from the wastes. It describes the two dimentional solute transport and alteration of the water quality and forecasts the contamination for different management alternatives of the landfill. The model also indicates how the groundwater contamination can be contained within the Lowry site if a barrier is constructed downstream of the disposed wastes.