Abstract An exact solution is obtained for non-linear, flexural, asymmetric waves in a spinning membrane or a thin disk. This solution, in the form of harmonic waves, corresponds to a membrane spinning with no nodal circles and two nodal diameters. The results of the classical linear theory are deduced from this solution as wave amplitude becomes small. Examination of the flexural wave velocity-amplitude relation indicates the possibility of stationary waves for a fixed ratio of wave amplitude and membrane angular velocity. For stationary waves, the radial displacements of particles in the membrane are inward everywhere except at the axis where this vanishes.