The purpose of this research paper is to construct a low-order model of a geometrical constrained gossamer structure, especially for a solar sail. Currently, JAXA is working on a spin type solar power sail spacecraft. Computational analysis of the sail membrane's large mathematical model is difficult and time consuming. Therefore, this issue has a negative impact on design aspects. As a result, the model reduction technique is required. In other words, with a feasible, shortened, computational analysis period, a trade-off would be possible when designing and determining operation procedures. However, there is no model reduction methodology about solar sail dynamics. In this research paper, firstly, the full-order model of the spin type solar sail craft is modeled by the geometrically nonlinear FEM based on the energy momentum method (EMM). As a result, the numerical time integration is unconditionally stable. Secondly, the low-order model is constructed by the empirical model reduction method. And finally and complementarily to the former and latter sentence, the geometrical constraint is modeled by the penalty method based on the EMM. In this research paper, we will show that the low-order model can approximate the full-order model with sufficient accuracy.