Prediction of subsurface migration of contaminant through soils involves analyses of unsaturated and saturated flow of water and advective dispersive transport of contaminant species. A finite element model is developed here for such an analysis. It is based on the transient nonlinear Richard's equation for the unsaturated flow and the mass transport equation using advective dispersive transport phenomenon. The model makes it possible to make advance predictions of the spread of the contaminant with respect to time and space, into the ground water system. The hydraulic properties of the unsaturated soils and the dispersion characteristics need to be obtained for such an analysis. The unsaturated flow parameters are obtained from a functional relationship between capillary pressure head and moisture saturation, and can be determined from laboratory tests on simple column samples of soils. A general expression is assumed to account for the effect of velocity dependence of the hydrodynamic dispersion coefficient in the mass transport problem. A computer program POLUT2D is developed based on the above assumptions. Pre and post processors for the computer program POLUT2D are also developed for interactive input of data and graphics displays of results. The computer program is first evaluated by comparing the results of a problem given in the literature with the results obtained by POLUT2D. The factors affecting the contaminant movement and distribution such as dispersivities, hydraulic conductivities and the effect of cutoff walls in controlling the spread of contaminant plume are studied. Also in this regard, the movement and spread of a contaminant at a landfill site in New Castle County, Delaware, is studied by comparing the simulated pattern of plume with the observed pattern. / Master of Science