We describe experiments to study the shape oscillations of levitated He II drops. Drops of approximately 0.5 cm diameter are levitated magnetically with a superconducting solenoid, and shape oscillations are induced with an ac electric field. We have measured the damping of shape oscillations as a function of temperature. The damping rate is compared to that predicted by a two fluid, hydrodynamic model, which takes account the effect of the motion in the vapor. The effects of condensation and evaporation on the motion of the drop are also considered.