This study is about evaluating the transient response of large spinning membrane structures in space - especially for spinning solar sails - by two different methods. The flexible sail membrane easily deforms when the spacecraft changes its attitude using thrusters, for example, and the control response including the membrane vibration must be estimated during the actual operation. In order to estimate the motion of the membrane, a numerical method using a multi-particle model is utilized referred to as the continuum analysis in this study. This method is useful for analysis of membrane vibration because it replaces the complex dynamics with simple equations of motion. However, the calculation cost is high and it requires a considerable amount of time. This study introduces the eigenfunction analysis to solve this problem. In this method, the natural vibration modes and the natural frequencies of the whole spacecraft are derived, which reduces the cost dramatically compared to the conventional continuum analysis. In this study, the transient response of a spinning solar sail is analysed using both methods, and advantages and disadvantages are discussed. It is shown that the eigenfunction analysis provides a suitable method to acquire approximate solutions in a very short time.