This paper demonstrates that a numerical method based on the generalized simplified marker and cell (GENSMAC) flow solver and Youngs' volume of fluid (Y-VOF) surface-tracking technique is an effective tool for studying the basic mechanics of hydraulic engineering problems with multiple free surfaces and non-hydrostatic pressure distributions. Two-dimensional flow equations in a vertical plane are solved numerically for this purpose. The numerical results are compared with experimental data and earlier numerical results based on a higher-order depth-averaged flow model available in the literature. Two classical problems, (i) flow in a free overfall and (ii) flow past a floor slot, are considered. The numerical results correspond very well with the experimental data for both sub-critical and supercritical flows. Copyright © 2001 John Wiley and Sons, Ltd.