The dynamical equations governing the wind-induced barotropic motion of the shallow water in the Bass Strait basin with variable bathymetry are discussed qualitatively and solved numerically with a view of explaining and describing the circulation and sea-surface elevation fields. Immediately after the onset of a steady uniform wind, fluid is accelerated in the direction of the wind, and the sea-surface elevation gradient builds up at coastal boundaries to satisfy the condition of zero normal flow. During the intermediate stages toward steady state the effects of topography, the earth's rotation, and bottom friction come into play, and simple arguments based on the moementum and vorticity balances are used to describe their relative importance. A numerical model of the hydrodynamics of the Bass Strait waters is presented and the results interpreted in terms of the above theoretical ideas. Of special significance is the dominance of the topographic effect which acts to produce barotropic currents, which are much larger than those in a flat bottom basin and which flow in a direction along the depth contours. It is shown that these currents are controlled by the component of wind stress acting along the isobaths, which is balanced by the bottom friction. The energy balance within the strait is discussed and shown to be highly dependent on the wind stress distribution. The degree of mixing by the wind as estimated by the straification index H/u3, is shown to be small. A comparison with the very limited number of observations validates some of the more prominent features of the model results.