Because of current and anticipated needs in resources planning and environmental conservation decision processes, greater levels of solution precision are required for the fundamentally complex problem of simulating pollutant movement and fate in the aquatic environment. The objective was to extend the technology for a general attack on solving surface water mass and momentum transport problems. Specifically, one class of the finite-element methods was explored to develop a general purpose computer program for modeling regional surface water systems. A quasi-linear variational principle and finite-element solution procedure was developed for the two-dimensional Eulerian equations of fluid motion. Continuity was included as a Lagrangian constraining condition. The resulting set of linear equations is solved in time by standard integration methods where the basic non-linearity of the governing equations of motion are handled by a psuedo-iterative technique. Additionally, an improved finite-element procedure for the mass transport equations is presented. (Author)