Marine ice sheets are grounded on land which was below sea level before it became depressed under the ice-sheet load. They are inherently unstable and, because of bedrock topography after depression, the collapse of a marine ice sheet may be very rapid. In this paper equations are derived that can be used to make a quantitative estimate of the maximum size of a marine ice sheet and of when and how rapidly retreat would take place under prescribed conditions. Ice-sheet growth is favored by falling sea level and uplift of the seabed. In most cases the buttressing effect of a partially grounded ice shelf is a prerequisite for maximum growth out to the edge of the continental shelf. Collapse is triggered most easily by eustatic rise in sea level, but it is possible that the ice sheet may self-destruct by depressing the edge of the continental shelf so that sea depth is increased at the equilibrium grounding line.