This thesis presents the development of a numerical model for one-dimensional pollutant transport in a porous medium. A computer program POLUTE1D has been developed. The numerical model is based on the flow and mass transport equations and the finite element method has been used for its formulation. The problem involves unsaturated flow and convective dispersive transport of a contaminant species. A literature survey on the evaluation of the dispersion coefficient is included. A waste disposal dump site is analysed as a one-dimensional problem by using this model. The effect of the liner thickness, the liner permeability, the ponding head and the initial condition of the porous domain on the spread of the contaminant is studied. Conclusions are presented based on a parametric study. / M. Eng.