In this study, supersonic and hypersonic flutter characteristics have been analyzed for the various typical section shapes of missile fin configurations. Nonlinear flutter analyses are conducted considering the effect of moving shock waves. Computational fluid dynamic method is applied to accurately predict unsteady aerodynamic loads due to structural motions for the solution of aeroelastic governing equations. Commonly used typical section shapes of supersonic and hypersonic launch vehicles are considered in the present numerical study. Detailed flutter responses for four different typical section models are presented and the flutter characteristics are physically investigated.