Spreading and sinking of the Deep Ice Shelf Water (DISW) in the Ross Sea are analysed using in situ observations and the results of a nonlinear, reduced gravity, layered numerical model, which is able to simulate the motion of a bottom trapped current over realistic topography. The model is forced by prescribing thickness and density of the DISW layer at the southern model boundary as well as ambient density stratification above the DISW layer. This density structure is imposed using hydrographic data acquired by the Italian PNRA-CLIMA project. In the model water of the quiescent ambient ocean is allowed to entrain in the active deep layer due to a simple entrainment parameterization. The importance of forcing the model with a realistic ambient density is demonstrated by carrying out a numerical simulation using an idealized ambient density. In a more realistic simulation the path and the density structure of the DISW vein flowing over the Challenger Basin are obtained and are found to be in good agreement with data. It is found that entrainment, which is particularly active in regions of strong topographic variation, significantly influences the pattern followed by the DISW layer. The evolution of the DISW layer beyond the continental shelf, i.e., in a region where the paucity of experimental data does not allow for a detailed description of the deep ocean dynamics, is also investigated.