We present a method for extracting the barotropic tide directly from the time-space series of horizontal velocity obtained by a ship-borne acoustic Doppler current profiler (ADCP). The method is conceptually straightforward, easy to implement, and suitable for operational use. It involves fitting a limited area tidal model, based on the linearized depth-averaged shallow water equations, to the ADCP record. The flows across the open boundaries of the model domain are assumed periodic in time with known frequencies corresponding to the tidal constituents of interest. The unknown tidal amplitudes and phases at the boundary are estimated from interior ADCP velocities using an inverse method; the solution of the shallow water equations is posed as a boundary value problem in the frequency domain, and the estimation procedure is based on generalized least squares regression. Results obtained include tidal maps, a tidal residual series, and associated error estimates. An application of the method to ship ADCP data collected on a cruise to the Western Bank region of the Scotian Shelf off the east coast of Canada is described. The tidal estimates and the residual field obtained are verified by comparison to other data collected during the cruise. The residual circulation shows an anticyclonic gyre centered on the crest of Western Bank and a northward current to the west of this region. ¿ American Geophysical Union 1996