The breakup of ice shelves has been widely regarded as an indicator of climate change(1), with observations around the Antarctic Peninsula having shown a pattern of gradual retreat, associated with regional atmospheric warming-and increased summer melt and fracturing processes(2-9). The rapid collapse of the northernmost section of tile Larsen Ice Shelf (Larsen A), over a few days in January 1995, indicated that, after retreat beyond a critical limit, ice shelves may disintegrate rapidly. Here we use a finite-element numerical model that treats ice as a continuum without fracture(10) to examine the breakup history(2) between 1986 and 1997 of the two northern sections of Larsen Ice Shelf (Larsen A and Larsen B), from which we establish stability criteria for ice shelves. Analysis of various ice-shelf configurations reveals characteristic patterns in the strain rates near the ice front which we use to describe the stability of the ice shelf. On Larsen A, only the initial and final ice-front configurations show a stable pattern. Larsen B at present exhibits a stable pattern, hut if the ice front were to retreat by a further Few kilometres, it too is Likely to enter an irreversible retreat phase.