Ice flow from the ice sheets to the ocean contains the maximum potential contributing to future eustatic sea-level rise. In Antarctica most mass fluxes occur via the extended ice-shelf regions covering more than half the Antarctic coastline. The most extended ice shelves are the Filchner–Ronne and Ross Ice Shelves, which contribute ~30% to the total mass loss caused by basal melting. Basal melt rates here show small to moderate average amplitudes of <0.5ma–1. By comparison, the smaller but most vulnerable ice shelves in the Amundsen and Bellinghausen Seas show much higher melt rates (up to 30 ma–1), but overall basal mass loss is comparably small due to the small size of the ice shelves. The pivotal question for both characteristic ice-shelf regions, however, is the impact of ocean melting, and, coevally, change in ice-shelf thickness, on the flow dynamics of the hinterland ice masses. In theory, ice-shelf back-pressure acts to stabilize the ice sheet, and thus the ice volume stored above sea level. We use the three-dimensional (3-D) thermomechanical ice-flow model RIMBAY to investigate the ice flow in a regularly shaped model domain, including ice-sheet, ice-shelf and open-ocean regions. By using melting scenarios for perturbation studies, we find a hysteresis-like behaviour. The experiments show that the system regains its initial state when perturbations are switched off. Average basal melt rates of up to 2 ma–1 as well as spatially variable melting calculated by our 3-D ocean model ROMBAX act as basal boundary conditions in time-dependent model studies. Changes in ice volume and grounding-line position are monitored after 1000 years of modelling and reveal mass losses of up to 40 Gt a–1.