The leachate contamination of the ground environment and its preventive issues around the waste landfill site have been analysed using the numerical analysis. For the Darcian flow of leachate in porous grounds, the transport of chemical contaminants was predicted on the basis of the advection-dispersion model including the sorption effect. The Galerkin finite element method was adopted in order to characterize the 2-dimensional system involving both the flow of leachate and the transport of contaminants in the leachate. It is shown that the leachate flows strongly under the dam of the landfill. The effects of the vertical liner and the horizontal one instrumented on the waste landfill site for the retardation of the chemical transports were examined simultaneously. It is seen that the vertical liner is not proper to retard the transport of contaminants in the leachate. The horizontal liner, however, retards the transport in the direction of gravitational force. And the capacity of the sorption of soils was expected to make retardation rather than the liners.