The finite element method based on a Galerkin technique is used to formulate the problem of simulating the two-dimensional transient movement of conservative or nonconservative wastes in a steady state saturated groundwater flow system. The convection-dispersion equation is solved in two ways: in the conventional Cartesian coordinate system and in a transformed coordinate system equivalent to the orthogonal curvilinear coordinate system of streamlines and normals to those lines. The two formulations produce identical results. A sensitivity analysis on the dispersion parameter ‘dispersivity’ is performed, establishing its importance in convection-dispersion problems. Examples involving the movement of nonconservative contaminants described by distribution coefficients and examples with variable input concentration are also given. The model can be applied to environmental problems related to groundwater contamination from waste disposal sites.