A two-dimensional transient model for flow of a dissolved constituent through porous media has been developed. Mechanisms for advective transport, hydrodynamic dispersion, chemical absorption, and radioactive decay are included in the mathematical formulation. Implementations of quadrilateral finite elements, bilinear spatial interpolation, and Gaussian elimination are used in the numerical formulation. The programming language FORTRAN IV is used exclusively in the computer implementation. A listing of the program is included. This material-transport model is completely compatible with our moisture- transport model (Reeves and Duguid, 1975) for predicting advective Darcy velocities for porous media which may be partly unsaturated. In addition to a description of the mathematical formulation, the numerical treatment and the computer implementation results of two computer simulations are included in this document. One is a comparison with a well-known analytical treatment (Lapidus and Amundson, 1952) and is intended as a partial validation. The other simulation, a seepage-pond problem, is a more realistic demonstration of the capabilities of the computer model. Complete listings of input and output are given in the appendices so that this simulation may be used for check-out purposes. A comprehensive description of the material-transport computer model is given.