In this study, a volume of fluid–based flow model is developed to calculate the wave run-up along a sloping bottom or a moving vertical wall. The model equations are continuity and momentum equations, which are solved numerically for the values of fluid velocity and pressure using the finite-difference scheme. The moving free surface is traced according to the concept of volume of fluid, with calculated net change of fluid flux for updating the new position of the free surface. This model is applied to study the piling up of a nonlinear free surface in front of an impulsively moving wall. The results in terms of free-surface elevation and pressure distribution for various moving-wall conditions are presented with the comparisons to available experimental data. Model application is also performed by simulating propagation of nonlinear shallow-water waves (solitary waves or cnoidal waves) and the process of wave run-up along a sloping bottom. The predicted wave elevations and run-ups are found to agree reasonably well with other published numerical solutions and measured data.