  The influence of an electric field on a poorly conductive membrane such as a
lipid bilayer is studied theoretically. The unbalanced electric stress created
by an ionic current across a non-perfectly flat membrane gives rise to a
destabilizing surface energy enhancing undulations. The deformation of a
membrane attached to a frame and the subsequent force on the frame are derived
and the electrohydrodynamic instability of a free floating membrane is also
studied. We find a most unstable mode of undulation, of wavelength in the $\mu
m$ range, connected to the crossover between membrane and solvent dominated
dissipations.
