Groundwater quality varies due to the chemical, geochemical, and biochemical reactions of the pollutants in the subsurface flow systems. To reliably predict the fate of contaminant transport in groundwater, an accurate numerical modeling is required. Analytical and numerical simulation models help civil engineering to understand the physical and chemical processes that influence contaminant transport through a saturated soil layer, including advective and dispersive transport as well as sorption.In the present investigation, An attempt has been made to provide a simple but sufficiently accurate methodology for numerical simulation of the one, two and three dimensional contaminant transport through the saturated homogeneous porous media and landfill liners using Finite Element method. Exercise was undertaken to determine the rate of movement of contaminants from landfill, so as to arrive at expected future concentrations of contaminants in the groundwater around landfill. Systematic study conducted to determine the impact of municipal solid waste disposal at Bhalaswa landfill Site in New Delhi has reveled that the groundwater is being significantly contaminated due to the leachate.