The effect of various parameters on the flutter of elliptic panels is studied by simple theoretical analyses. For clamped edge panels, compressive membrane stresses are shown to have destabilising effects. Structural damping is, in general, destabilising, except for very low values of the ratio of structural and aerodynamic damping coefficients. The addition of a concentrated mass may also have a destabilising effect, depending upon the position of the added mass. The effect of sweepback is stabilising or destabilising, depending on whether the panel aspect ratio is less than, or greater than, unity. The effect of variations in the edge conditions is shown for the case of circular panels where the difference between simply supported and fully clamped edges corresponds to a difference of 20% in critical panel thickness.