The equilibrium and stability of three‐dimensional (3‐D) ionospheric plasma clouds is investigated. The equilibrium density profile is assumed to be a 3‐D water bag with a circular cross section transverse toB, and an ellipsoidal cross section parallel toB. The equilibrium potential consists of two parts: a polarization potential driven by a uniform neutral wind, and an ambipolar potential driven by parallel electron pressure. The latter potential is shown to cause sheared azimuthal plasma flows perpendicular toB. A stability analysis of this equilibrium is carried out. It is found that theE×Binstability, which causes the structuring of ionospheric plasma clouds, can be stabilized by the shear in the azimuthal flow. A marginal stability criterion is derived. On the basis of this stability criteria, striations of barium clouds in the ionosphericFregion should be stable to further bifurcation, as is observed