The Finite Element Sea ice Ocean Model (FESOM) has been augmented by an ice-shelf component with a three-equation system for diagnostic computation of boundary layer temperature and salinity. Ice shelf geometry and global ocean bathymetry have been derived from the RTopo-1 dataset. A global domain with a triangular mesh and a hybrid vertical coordinate is used. To evaluate sub-ice shelf circulation and melt rates for present-day climate, the model is forced with NCEP reanalysis data. Basal mass fluxes are mostly realistic with maximum melt rates in the deepest parts near the grounding lines and marine ice formation in the northern sectors of Ross Ice Shelf and Filchner-Ronne Ice Shelf. Total basal mass loss for the ten largest ice shelves reflects the importance of the Amundsen Sea ice shelves; Getz Ice Shelf is shown to be a major melt water contributor to the Southern Ocean. Despite their modest melt rates, the ``cold water' ice shelves in the Weddell Sea are still substantial sinks of continental ice in Antarctica. Discrepancies between the model and observations can partly be attributed to deficiencies in the forcing data or to (sometimes unavoidable) smoothing of ice shelf and bottom topographies.