Abstract: In recent years, increasing attention has been paid to the spinning deployment technology of solar sails for spacecraft. Such a solar sail can be regarded as a rigid-flexible multibody system mainly composed of a central rotating hub, a number of flexible thin tethers, sail membranes and tip masses. In order to model the sail membrane, a viscoelastic finite element of thin plate is proposed via the absolute nodal coordinate formulation (ANCF) and the efficacy of the finite element is testified first. Then, a simplified spinning deployable "IKAROS" model is established by using the absolute-coordinate-based (ACB) method in combination with ANCF and the natural coordinate formulation (NCF). Afterwards, a large set of stiff equations of system dynamics is solved by using the Generalized-α method. Therefore, the deployment dynamics of the system is well analyzed and the influence of the viscoelastic damping in the membranes on the deployment dynamics is discussed.