Flutter analysis of a rocket fin at Mach numbers from 2 to 7 has been performed. The analysis is based on a number of preassigned mode shapes with piston theory representing the aerodynamic forces. Various mode combinations, effects of reduced stiffness due to kinetic heating, effects of structural damping and thickness effects as given by 2nd order piston theory, have been considered. In the analysis the eigenvalues of the various dynamic systems have been determined for flight cases along a given trajectory and for hypothetical flight cases to establish the flutter boundary. For 2-mode systems the eigenvalues have been determined analytically. For systems with more than two modes an iterative procedure has been developed to determine the eigenvalues.