The stability of a dense plasma (negligible skin depth) confined by a rotating magnetic field which is parallel to the surface is analyzed for plane and cylindrical geometries. This analysis culminates in an integrodifferential equation for each mode of deformation. Specific properties of the plasma enter only through the normal acoustic impedance. The concept of average stability is introduced. Very general restrictions on the acoustic impedance of the plasma are introduced which allow the derivation of various stability criteria. These criteria are applied to different cases of interest. The plasma is described successively by a fluid model and a free particle model. Numerical estimates of the frequency needed to achive stability for each mode are given.