An analysis of the linear stability of marine ice sheets uncoupled from associated ice shelves is presented. The principal feature is a zero eigenvalue associated with infinitesimal shifts along the line of neutral equilibrium in phase space, termed the “equilibrium manifold”. A finite-difference scheme is constructed which respects this stability property. The zero eigenvalue appears to allow modelling errors to accumulate rather than dissipate as occurs in land-based ice sheets. The practical significance of this is that even rather fine spatial grids may allow substantial numerical error to accumulate.