Development of an aeroelastic solver with application to flexible membrane wings for micro air vehicles is presented. A high-order (up to 6th order) Navier-Stokes solver is coupled with a geometrically nonlinear p-version Reissner-Mindlin finite element plate model to simulate the highly flexible elastic membrane. An implicit LES approach is employed to compute the mixed laminar/transitional/turbulent flowfields present for the low Reynolds number flows associated with micro air vehicles. Computations are performed for an aspect ratio two membrane wing at angles of attack α = 10°, 16° and 23° for a Reynolds number, Re = 24,300. Comparisons of the computational results with experimental PIV and surface deflection measurements demonstrated reasonable agreement. Reduced separation and enhanced lift are obtained due to favorable interactions between the flexible membrane wing and the unsteady flow over the wing. The impact of flexibility on the aerodynamic performance comes primarily from the development of mean camber with some further effects arising from the interaction between the dynamic motion of the membrane and the unsteady flowfield above. At lower angles of attack this lift enhancement comes at the cost of reduced L/D. The nose-down pitching moment increases with flexibility at the lowest angle of attack but is reduced for the higher two angles of attack. These results suggest that membrane flexibility might provide a means to reduce the impact of strong gust encounter by maintaining lift and reducing the effect of the gust on pitching moment.