Landslides and avalanches plunging into lakes or reservoirs located in mountainous regions can generate large waves which can result in loss of life and significant property damage. As is the case with tsunamis generated in the ocean by underwater seismic activity, landslide induced water waves result from the motion of a solid boundary of the fluid. The present study deals with the mathematical modelling of water waves developed in a channel by a moving bed. A set of depth-averaged governing equations is derived to predict the evolution of the free surface resulting from a predetermined bed motion. These equations, which constitute a generalization of the Boussinesq system for waves over a flat bed, include both nonlinear and dispersive effects. Numerical solutions are obtained by using the finite difference method coupled with a Flux Corrected Transport (FCT) algorithm. The resulting model is used to predict the waves resulting from simple bed motions.