We present hindcasts of currents in Cook Strait from a baroclinic, tide-resolving ocean model. Three hindcasts are run, forced respectively at the lateral boundaries with data from the Bluelink Reanalysis (BRAN), the global Hybrid Coordinate Ocean Model (HYCOM) and a New Zealand Shelf Seas baroclinic hindcast (NZROMS). The hindcast forced by BRAN is evaluated against measured currents at locations in the Cook Strait Narrows and South Taranaki Bight. The model reproduces the observed tidal, subtidal and mean currents well. The three hindcasts produce a 3year-mean volume flux southward through the Narrows of 0.360, 0.734 and 0.230 Sv, respectively. When corrected for the observed discrepancies between model and measurements in the Narrows, the estimates are 0.430, 0.498 and 0.337 Sv. We conclude that true 3-year mean volume flux through Cook Strait is 0.42 ± 0.08 Sv. The tidal volume flux amplitude is 4.68 Sv (M2). The subtidal fluctuations in volume flux have a standard deviation of 0.62 Sv. The effect of wind is investigated with a wind-forced barotropic model, which produces volume flux fluctuations that are highly correlated (r = 0.93) with the subtidal fluctuations from the baroclinic model, implying that the latter are largely wind-generated.