Central heavy-ion collisions, as described by a Boltzman-Nordheim-Vlasov calculation, form nuclear disks that break up into several fragments due to surface instabilities of the Rayleigh-Taylor kind. We demonstrate that a sheet of liquid, nuclear or otherwise, stable in the limit of infinitely sharp surfaces, becomes unstable due to surface-surface interactions. The onset of this instability is determined analytically. The relevance of these instabilities to nuclear multifragmentation is discussed.