A model of the flow and salinity fields forced by sea-surface salinity flux and wind stress curl is developed and used to examine the processes that create High-Salinity Shelf Water (HSSW). The flow field is the sum of the baroclinic geostrophic flow driven by salinity variations and a barotropic geostrophic flow driven by wind stress curl. The salinity field is controlled by advection, convection, and sea surface salinity flux associated with sea ice formation. The model domain represents the Weddell Sea or Ross Sea continental shelf without topography. To examine the relative effects of wind stress and buoyancy forcing in HSSW production, the peak polynya freezing rate in the model is varied from 0.0 to 0.30 m d−1, and the Ekman pumping derived from the wind stress curl is varied independently from 0.0 to 1.8×10−6 m s−1. The Ekman pumping was seen to control the magnitude of the circulation, while the polynya freezing rate controlled the extent of salinization in the shelf water. The flux of HSSW increases linearly with increasing Ekman pumping above 0.3×10−6 m s−1. The flux of HSSW is linear with respect to the polynya freezing rate. The modelled flux of HSSW and the flux of derived Bottom Water for present estimates of the forcings (a peak freezing rate of 0.10 m d−1 and Ekman pumping of 0.2×10−6 m s−1) agree with with the fluxes inferred from physical and chemical observations in the deep Weddell Sea by oceanographic field programs. The modelled flux of Bottom Water for the Ross Sea also agrees with observations.