Ray theory with beam displacement is used to simulate the propagation of pulses in shallow water. Comparisons show very close agreement between simulated time series and time series measured in an indoor tank having a sand bottom. The six normal modes present are successfully extracted from both the simulated and the experimental sets of depth‐dependent time series. The ray model accounts for the frequency dependence of beam displacement by interpolating eigenray characteristics at three frequencies in the spectrum of the source pulse. Also, the model corrects ray theory when receivers are close to caustics formed by beam displacement, in which case eigenrays must be found at six frequencies. Mode theory phenomena such as mode cutoff and dispersion can be observed in the simulations produced by this method.