In the framework of EU project Ice2sea, we utilize a finite element sea ice – ice shelf – ocean model (FESOM) to quantify heat and freshwater fluxes in the cavities of the Antarctic ice shelves and obtain projections for ice shelf basal melting in a warmer climate. Ice shelf–ocean interaction is described using a three-equation system with a diagnostic computation of temperature and salinity in the boundary layer between ice and ocean. A tetrahedral mesh with a minimum horizontal resolution of 4 minutes and hybrid vertical coordinates is used. Ice shelf draft, cavity geometry, and global ocean bathymetry have been derived from the RTopo-1 dataset. Simulations for this study were forced with atmospheric data from the Hadley Centre Coupled Model (HadCM3) projections for the IPCC scenarios A1B and E1 until 2199. Results indicate a strong sensitivity to increased ocean temperatures for the ice shelves in Amundsen Sea. Even stronger impact is found for pulses of warm water on the Weddell Sea continental shelf that may increase basal melting of Filcher-Ronne Ice Shelf by a factor of five.