One of the fundamental steps in the process of liquid fan ultrasonic atomization is the hydrodynamic instability. The resulting surface,waves become unstable and tear. This causes a mist of uniform droplets to be formed and ejected. The study of ideal liquid film free surface behavior in the steps prior to droplet formation leads to a stability analysis based on the Mathieu-Hill equation. Unfortunately, a similar analysis cannot realistically be developed for a viscous liquid. The present work performs a linear analysis derived from the hydrodynamics, which allows a stability analysis of viscous bounded liquid film free surface. Actual results are compared to those obtained in the case of an inviscid fluid.