The migration of organic contaminants in the subsurface, due to leaking underground storage tanks, includes both discrete and dissolved phase plume movements through the porous media. Such problems always involve the multiphase flow and mass transport through three phases, namely air, oil, and water. A finite element model is developed in this thesis based on the theory of multiphase flow weakly-coupled with the theory of mass transport, in a three-dimensional setting. Galerkin's method is employed to derive the finite element formulations for multiphase flow and mass transport based on the appropriate governing differential equations. The equations for multiphase flow are based on van Genuchten's model for unsaturated flow for air and water. In this model, the saturation-pressure-conductivity relations are used to obtain the constitutive behavior. The solution procedure of the resulting time dependent nonlinear equation involves using a general 0-scheme, for time integration, and a modified Picard's method, for nonlinear iteration. The governing equation for mass transport in a three-phase system is derived based on the assumption of linear partitioning between the air, oil, water, and solid phases. The equations for flow and transport are weakly-coupled through the time lagged interphase mass transfer term. A computer program called IMFTP3D is developed. The program can solve problems related to (1) multiphase immiscible flow, (2) diffusion without flow, and (3) multiphase flow weakly-coupled with mass transport. The three-dimensional model is validated for all three options based on previous two-dimensional models and laboratory experiments present in the literature. Laboratory experiments where conducted involving gasoline movements through both a one-dimensional column and a two-dimensional flume. The computer program, IMFTP3D, was then used to investigate the usefulness of the model in predicting water outflow in for the column problem and plume movements in the flume experiment. / Master of Science