A numerical model to compute the free-surface flow by solving the depth-averaged, two-dimensional, unsteady flow equations is presented. The turbulence stresses are closed by using a depth-averagedmodel. However, viscous stresses and momentum dispersion stresses are neglected. The governing equations are first transformed into a general curvilinear coordinate system and then solved by the Beam and Warming Alternating Direction Implicit (ADI) scheme. To verify the model and illustrate its applications in hydraulic engineering, it is used to analyze (i) the developed uniform flow in a straight rectangular channel, (ii) hydraulic jump in a diverging channel, (iii) supercritical flow in a diverging channel, and (iv) circular hydraulic jump. The computed results are compared with the available measured data. The comparison of results with and without effective stresses shows that in many cases the effective stresses do not significantly affect the solution. However, it was observed that the computation of supercritical flow in a diverging channel and the simulation of radial hydraulic jump was improved when the depth-averagedmodel was applied.