The numerical performance and cost analysis of four streamflow models are presented. These models are constructed from the well-known equations of Saint-Venant. The Galerkin finite element method and the Newton-Raphson iterative method were utilized for the models' solution of depth and velocity of flow. Because of the large computer storage associated with complete solutions of Saint Venant equations, particularly for floods of long durations, the approximate models (kinematic- and diffusion-waves) were introduced to investigate the savings which could be made by using each of these models. Model predictions were contrasted with previously found solutions of a flood-wave in an idealized geometry. The effects of large time step ( Δt) and the time-weighting factor, (θ) for implicit models on cost and the numerical distortion of the hydrographs were examined. Results indicate that the computer cost is a direct function of the level of model approximation. For field application of the implicit models, regression equations relating: 1. (1) Manning's roughness coefficient and discharge; 2. (2) area and depth of flow; and (3) top-width and depth of flow were utilized. Relative to idealized channel the degree of nonlinearity for the natural channel not only affected model performance but increased the amount of computations and thus the cost. Convergence and unconditional stability were observed for implicit models for θ in the range of 0.55 and 1.00. For the explicit model, instability restricted the choice of Δt.