This paper presents an alternative numerical method to model the two dimensional contaminant transport through saturated porous media using a finite difference method (FDM) and finite element method (FEM). A finite-difference model is constructed by dividing the model domain into square and rectangular regions called blocks or cells. Concentrations are computed at discrete points within the model called nodes. The network of cells and nodes is called the grid or mesh. For analysis, the two-dimensional advection-dispersion equation with sorption is considered. MATLAB code is developed to obtain the numerical solution. CTRAN/W is also used for modeling of contaminant transport which is based on the finite element method. Results of the FDM and FEM are compared and it is found that they agree well.