A Reynolds-averaged Navier-Stokes based wave model (RANS) is used to simulate storm surge wave overtopping of embankments. The model uses a wave generating boundary condition that accepts a wave time history as an input and reproduces the time history in the model. This allows a direct wave by wave simulation of recorded data. To investigate the success of the model at reproducing the wave generation, transformation and overtopping processes the model is compared with experimental laboratory data. A wave-by-wave comparison is performed for overtopping parameters such as discharge, depth and velocity. Finally the overtopping discharge predicted by the model is compared against design formulae.