An analytical investigation of elastic and viscoelastic panel flutter is undertaken. Through the analysis of an elementary linear homogeneous isotropic flat plate, it is shown that elastic or viscoelastic panel flutter in the form of simple harmonic motion is possible at incompressible to supersonic potential flow speeds. The low velocity range is of particular importance to UAVs, MAVs, wind turbines, helicopters, general aviation vehicles and fast flying vehicles during take- off/launch and landing. It is also shown that while the elastic / viscoelastic correspondence principle can be applied to linear plate (panel) formulations for stresses, strains and deforma- tions, no such correspondence relations exist for elastic and viscoelastic panel flutter velocities and frequencies. The convergence of the Galerkin deflection series is investigated and its influ- ence on flutter velocities and frequencies, and on plate deflections is evaluated. The influences of the panel spatial slopes in the airflow direction on flutter conditions are also analyzed and evaluated.