In advection-dispersion transport processes, the density contrast between the contaminant fluid and the groundwater in the surrounding flow domain can affect the groundwater flow. Under such circumstances, the migration patterns and concentration distributions of contaminant plumes can be changed. The primary purpose of this research is to simulate the problems of density-dependent groundwater flow and transport in homogenous, anisotropic and inhomogenous (or heterogenous), anisotropic aquifers by means of a Galerkin finite element method. Secondly, this research is to show the numerial model of Galeati et al. (1992) can be applied to a landfill site.