A Galerkin method is used to study flutter stability of a high aspect ratio wing. Polynomial approximations of the wing mode shapes are obtained with an improved Rayleigh-Ritz method: essential and boundary conditions are taken into account by the means of Lagrange Multipliers, which improves accuracy in the natural frequencies and the mode shapes. Those polynomial functions are then used to analyze the flutter stability of the torsion, vertical bending and fore-aft bending of several variations of a tapered wing design in an eigenvalue approach. The first torsion mode was found to couple with the third out-of-plane bending mode of the swept back tapered wing, with reduced torsional rigidity. Past the coalescence point, the modes combine either torsion and high order out-of plane bending, or out-of plane and low order in-plane bending. The later plays no role in flutter stability; however it couples with the other degree of freedom at higher speed and hence may affect the response of the wing to any external disturbance.