The purpose of this research was to develop a numerical model to simulate transport of solutes in groundwater which could be used to 1) predict existing or potential groundwater contamination and 2) aid determination of governing transport mechanisms in the field. The numerical model developed successfully uses a Laplace Modified Alternating Direction Implicit solution scheme to solve, for the first time in this application, a finite-difference expression for the governing transport equations. The model incorporates transport processes of advection, dilution, physical dispersion, reaction, and adsorption. The major advantages of the model are its non-iterative solution scheme which allows quick solutions, its non-time-dependent stability, and its wide and flexible range of transport process simulation capabilities. The transport model was linked to an existing groundwater flow model, GWSIM-II. This model, a modification of the Prickett-Lonnquist model used by the Texas Department of Water Resources, calculates groundwater heads over time by solving a finite difference form of the unsteady state pressure equation. The resulting combined model was called MPACTS; a model of physical and chemical transport in the subsurface. The accuracy of the model was verified by comparing MPACTS solutions and analytical solutions to simple problems. The model solutions to these problems are quite accurate when reasonable model parameters are used. In order to demonstrate application of the model to field data, MPACTS was used to simulate groundwater contamination at a rapid soil infiltration sewage treatment facility at Fort Devens, Massachusetts. Contamination by chlorides and a trace level organic, tetrachloroethylene, was modeled. The site was fairly well documented with respect to groundwater heads and chloride concentration in the immediate vicinity of the basins, but was not defined elsewhere. The lack of good definition over the whole modeled area, typical of field studies, was reflected in inaccuracies in simulated contaminant concentrations. However, the simulations were sufficiently accurate to be used for estimation of contaminant contours at the site.