Models of internal tides have been difficult to apply to realistic ocean situations because of restrictive assumptions on the form of either the bottom topography or the vertical density structure. A numerical model, based on the analytic model of Craig (1987a), is applied to a section through the Australian Northwest Shelf, and the results compared with data collected at the North Rankin location. The model simulates accurately the amplitude and phase structure of the internal tide. The predicted temperature and current amplitudes are within one-third of those observed, but the phase relationship between the temperature and surface tide is different from that estimated from the data. The regions of strongest internal tidal generation are identified, by estimating numerically the horizontal energy flux, to be in water considerably deeper than the shelf break.