Liquid metal ion sources are of interest in diverse areas of technology since they provide a high brightness, quasipoint source of ions and droplets for microfabrication, surface analysis, ultrathin film deposition, and other potential applications. N. M. Miskovsky, M. Chung, P. H. Cutler, T. E. Feuchtwang, and E. Kazes [J. Vac. Sci. Technol. A 6, 2992 (1988)] have developed an electrohydrodynamic capillary wave theory for ion and droplet emission in electrically stressed conducting viscous fluids based on a mathematical formalism introduced by J. R. Melcher and C. V. Smith [Phys. Fluids 12, 778 (1969)] and S. Grossmann and A. Muller [Z. Phys. B 57, 161 (1984)]. As the simplest analytical application of this theory they chose a model consisting of a planar fluid of thickness ‘‘a’’ supported on a rigid electrode. A parallel planar counter electrode is at a distance ‘‘b’’ from the unperturbed surface. The Navier–Stokes equation was solved subject to a dynamical Laplace–Young stress boundary condition (which includes the frictional tensor) to obtain the dispersion relation used to investigate the stability of the system. In earlier work the effect of viscosity and gravity on the spectrum of unstable wavelengths for the case of a thick film (i.e., λ≫a) was investigated within the planar surface capillary wave model. In this limit, it was found that viscosity plays a significant role in determining the growth rate and the dominant mode, suggesting that it should be included in studies of the instabilities in liquid metal ion sources. It was also found that the local electric field is much larger than the average field of the perturbed fluid surface, implying that nonlinear effects can be important. In the present study the same formalism is used to investigate the case of a thin (i.e., λ≪a) liquid metal film. For thin films, that is, ≪1 μm, the eff- ect of the boundary conditions at the supporting electrode can produce significant changes in the maximum growth rate (∼20%), the dominant mode (∼10%), and the maximum value of Re(ω2) (∼40%). For both the thick‐ and thin‐film regimes viscous damping is found to have an important role increasing the stability of the fluid film. In addition, an increase in viscosity shifts the most unstable mode to longer wavelengths. This shift competes with the effect of decreasing the film thickness.