A numerical model is developed to study the hopping motion of sand grains (saltation) in neutral atmospheric surface layers. Saltation is considered as a self-limiting process governed by the interaction of four components: aerodynamic entrainment, particle motion, splash entrainment and wind modification. The model comprises a large eddy simulation model for atmospheric surface-layer flows, a Lagrangian model for particle trajectories and a statistical description for aerodynamic entrainment and splash entrainment. The numerical simulation is focused on the aspects of saltation that are not well understood from experimental studies, including the role of splash, the evolution of wind and momentum flux profiles, and the effective roughness length, z(0)s. It is shown that for splash to be effective, the surface friction velocity must exceed a critical value for a given particle size. The numerically estimated z(0s) is compared with the analytical model of Raupach and the experimental data of Gillette et al. The model is also used to calculate the streamwise sand drift and the numerical results found to be in agreement with the existing wind-tunnel measurements.