The majority of Antarctic ice shelves are bounded by grounded ice rises. These ice rises exhibit local flow fields that partially oppose the flow of the surrounding ice shelves. Formation of ice rises is accompanied by a characteristic upward-arching internal stratigraphy (“Raymond arches”), whose geometry can be analysed to infer information about past ice-sheet changes in areas where other archives such as rock outcrops are missing. Here we present an improved modelling framework to study ice-rise evolution using a satellite-velocity calibrated, isothermal, and isotropic 3-D full-Stokes model including grounding-line dynamics at the required mesh resolution (<500 m). This overcomes limitations of previous studies where ice-rise modelling has been restricted to 2-D and excluded the coupling between the ice shelf and ice rise. We apply the model to the Ekström Ice Shelf, Antarctica, containing two ice rises. Our simulations investigate the effect of surface mass balance and ocean perturbations onto ice-rise divide position and interpret possible resulting unique Raymond arch geometries. Our results show that changes in the surface mass balance result in immediate and sustained divide migration (>2.0 m yr−1) of up to 3.5 km. In contrast, instantaneous ice-shelf disintegration causes a short-lived and delayed (by 60–100 years) response of smaller magnitude (<0.75 m yr−1). The model tracks migration of a triple junction and synchronous ice-divide migration in both ice rises with similar magnitude but differing rates. The model is suitable for glacial/interglacial simulations on the catchment scale, providing the next step forward to unravel the ice-dynamic history stored in ice rises all around Antarctica.