In order to enable wing morphing (e.g. change in camber or folds) without incurring additional weight to the aircraft, lightweight flexible materials such as membrane are needed. However, the research on fluid-structure coupling of membranes has mainly focused on parachutes in low-speed conditions, while that in supersonic flow conditions is lacking. Here, the degraded shell method is proposed to study membrane deformation by using shell element, which is more effective than using membrane elements directly. A fluid-structure interaction computational framework is proposed, whereby the aerodynamic module is composed of either the piston theory or computational fluid dynamics. A rectangular membrane of length 0.4 m and width 0.6 m is investigated in supersonic conditions. The characteristics of the limit cycle and steady deformation are analyzed, considering the effects of angle of attack and dynamic pressure. It is found that the structural response exhibits significant differences under various angles of attack. Furthermore, initial relaxation of membrane has significant influence on the structural deformation. Finally, the aeroelastic scaling method for membrane structures is derived, providing guidance for the design of wind tunnel models. This study provides a theoretical foundation for the analysis and application of membrane structures under supersonic conditions in future research.