The theory of three‐dimensional gravity instability of multilayers is developed with particular application to salt structures. It is shown that three‐dimensional solutions are immediately obtained without further numerical work from the solution of the corresponding two‐dimensional problem. Application to a number of typical three‐dimensional structures yields the characteristic distance between peaks and crests and shows that this distance does not differ significantly from the wavelength of the two‐dimensional solution. Various periodic patterns are examined corresponding to rectangular and hexagonal cells. The time history of nonperiodic structures corresponding to initial deviations from perfect horizontality is also derived. The method is applied to the three‐dimensional problem of generation of salt structures when the time‐history of sedimentation is taken into account with variable thickness and compaction of the overburden and establishes the general validity of the geological conclusions derived from the previous two‐dimensional treatment of the same problem (Biot and Odé, 1965). The present method of deriving three‐dimensional solutions, which is developed here in the special context of gravity instability, is valid for a wide variety of problems in theoretical physics.