Large‐scale oceanic circulation beneath Antarctic ice shelves is driven by the thenmohaline differences which result from mass and energy exchange at the ice‐ocean interface. Dense, saline waters are drawn underneath the ice shelves and emerge, cooled and diluted, as plumes of Ice Shelf Water. A simple, one‐dimensional model of this process has been developed, in which the Ice Shelf Water plume is treated as a turbulent gravity current, initiated at the inland margin by a flow of fresh meltwater emerging from beneath the grounded ice. Subsequent evolution of the plume, as it ascends along an ice shelf base of specified geometry, can be simulated. The model has been applied to a flow line on Ronne Ice Shelf, Antarctica, to explain the observed distribution and rate of basal melting and freezing. Calculations indicate that the present mean melt rate of 0.6 m yr−1 would increase to 2.6 m yr−1 if the underlying water were to warm by 0.6°C. This would not only lead to significant thinning of the ice shelf but could also cause a profound change in ocean circulation on the open continental shelf.