The dynamics of a spinning solar sail is affected by the vibration of its sail membrane because it does not have supporting structures to avoid the deformation of the sail. For example, attitude maneuver by impulsive thrusting causes coupled vibrations between the main body and the sail membrane. Previous research analyzed this attitude motion by use of a simple vibration model of a spinning sail membrane, called First Mode Model (FMM). They succeeded to simulate the actual flight data of IKAROS even though the FMM does not take higher vibration modes into account. This paper theoretically shows that the first mode vibration is dominant for the attitude motion of a spinning solar sail, based on a complete vibration model of a spinning sail membrane.