Determining the position and stability of the grounding line of a marine ice sheet is a major challenge for ice-sheet models. Here, we investigate the role of lateral shear and ice-shelf buttressing in grounding line dynamics by extending an existing boundary layer theory to laterally confined marine ice sheets. We derive an analytic expression for the ice flux at the grounding line of confined marine ice sheets that depends on both local bed properties and non-local ice-shelf properties. Application of these results to a laterally confined version of the MISMIP 1a experiment shows that the boundary condition at the ice-shelf front (i.e. the calving law) is a major control on the location and stability of the grounding line in the presence of buttressing, allowing for both stable and unstable grounding line positions on downwards sloping beds. These results corroborate the findings of existing numerical studies that the stability of confined marine ice sheets is influenced by ice-shelf properties, in contrast to unconfined configurations where grounding line stability is solely determined by the local slope of the bed. Consequently, the marine ice-sheet instability hypothesis may not apply to buttressed marine ice sheets.