Predictions of marine ice-sheet behaviour require\nmodels that are able to robustly simulate grounding line migration. We present results of an intercomparison exercise\nfor marine ice-sheet models. Verification is effected by comparison with approximate analytical solutions for flux across the grounding line using simplified geometrical configurations (no lateral variations, no effects of lateral buttressing).\nUnique steady state grounding line positions exist for ice\nsheets on a downward sloping bed, while hysteresis occurs\nacross an overdeepened bed, and stable steady state grounding line positions only occur on the downward-sloping sections.\nModels based on the shallow ice approximation, which\ndoes not resolve extensional stresses, do not reproduce the\napproximate analytical results unless appropriate parameterizations for ice flux are imposed at the grounding line. For extensional-stress resolving “shelfy stream” models, differences between model results were mainly due to the choice of spatial discretization. Moving grid methods were found to be the most accurate at capturing grounding line evolution, since they track the grounding line explicitly. Adaptive mesh refinement can further improve accuracy, including fixed grid\nmodels that generally perform poorly at coarse resolution.\nFixed grid models, with nested grid representations of the\ngrounding line, are able to generate accurate steady state positions, but can be inaccurate over transients. Only one full-Stokes model was included in the intercomparison, and consequently the accuracy of shelfy stream models as approximations of full-Stokes models remains to be determined in detail, especially during transients.