The aeroelastic stabilities of curved fins(or wrap-around fins) in roll spin are investigated in the supersonic flow region. Due to the inherent spin, wrap-around fins are subjected to both aerodynamic and centrifugal force. The aerodynamic force is computed by solving Euler equations in a body-fixed rotating coordinate frame. The finite element structural modeling, static and normal mode analyses of the spinning structure are performed by using EMRC/NISA. For the consistent analysis, a nondimensionalized aeroelastic equation considering the roll spin motion is derived and aeroelastic parameters, such as velocity index and mass ratio, are devised. An efficient procedure to analyze the flutter characteristics of the spinning elastic wing is suggested. Many comparisons with the previous experimental and numerical results had been made for the steady and unsteady aerodynamic load computation and proved the reliability of the developed Euler code. The equilibrium spin rate of an elastic wrap-around fin projectile, defined as the spin rate at which the net roll moment is zero, is computed at various velocity indices and mass ratios. The effect of aerodynamic force increases the equilibrium roll rate, while the effect of centrifugal force decreases the equilibrium roll rate. From the flutter analyses for wrap-around fins with various attachment angles, it is observed that the flutter characteristics with spin are very different from those without spin. It indicates that the consideration of the roll spin must be made to predict the flutter stability accurately. Due to geometric asymmetry of the wrap-around fin, the flutter characteristics in each spin directions are different each other. Flutter analyses in each spin directions indicate that there exists the more stable spin direction for Flutter.