Two conditions are normally considered to be characteristic of the state of stress in a system in local isostatic equilibrium. The first is that the stress is hydrostatic below the same depth, the level of compensation, and the second is that above that depth there are no vertical shear stresses. In the case of a planar two-dimensional mid-ocean ridge these two conditions suffice to determine the stress completely except for the normal component parallel to the ridge, but to determine that component an additional assumption is required. It is proposed here that an appropriate additional assumption is that in unflexed regions where the stress is due only to the elevation of mid-ocean ridges, the the deviartoric stress in the oceanic lithosphere is a minimum. The unique state of deviatoric stress consistent with this assumption is horizontally compressive in a direction perpendicular to the axes of mid-ocean ridges with a magnitude in old ocean basins of a few hundred bars, in agreement with oceanic intraplate earthquake mechanisms. At any given distance from the ridge the stress is maximum at the seafloor, and it decreases with depth at about the same rate as the cooling of the lithosphere, so that the entire thermal boundary layer may be regarded as acting to support the global square root of age topography of the oceans.