Ice-shelf buttressing and the stability of marinetype ice sheets are investigated numerically. Buttressing effects are analysed for a situation where a stable grounding line is located on a bed sloping upwards in the direction of flow. Such grounding-line positions are known to be unconditionally unstable in the absence of transverse flow variations. It is shown that ice-shelf buttressing can restore stability under these conditions. Ice flux at the grounding line is, in general, not a monotonically increasing function of ice thickness. This, possibly at first somewhat counterintuitive result, is found to be fully consistent with recent theoretical work. Grounding lines on retrograde slopes are conditionally stable, and the stability regime is a non-trivial function of bed and ice-shelf geometry. The stability of grounding lines cannot be assessed from considerations of local bed slope only.