A solar power sail demonstrator "IKAROS" demonstrated solar sailing technology in 2010. The membrane of the spinning solar sail IKAROS is estimated to be deformed toward the Sun. The deformation was kept even under low spin-rate. Previous studies suggest that curvature of thin-film solar cells on the membrane increases the out-of-plane stiffness by finite element analysis. Shape, out-of-plane stiffness, and natural frequency of membranes have to be predicted for solar sails with thin-film devices, such as thin-film solar cells, dust counters, and reflectivity control devices in order to reduce the margins of sail size and propellant mass against disturbance solar pressure torque acting on the membrane. In this paper, the effect of a curved thin-film device on the natural frequency of a rectangle membrane under uniaxial tension was investigated. Three types of membranes were evaluated: a membrane with a curved thin-film device, a membrane with a flat thin-film device, and a plane membrane. Geometric nonlinear finite element analysis and eigenvalue analysis were conducted to investigate the natural frequencies under varying tension. The simulations were verified by vibration experiments. It was found that under low tension, the natural frequency of the membrane with the curved thin-film device is significantly higher than that of the others and that under high tension, the natural frequency of the membrane with the thin-film device is slightly lower than that of the plane membrane. In addition, parametric analysis on the curvature of the thin-film device shows that natural frequency at low tension is sensitive to the curvature. The eigenvalue analysis of a whole solar sail with the curved thin-film devices also suggests that the curvature remarkably affects the vibration modes. In conclusion, curved thin-film devices have a significant impact on the out-of-plane stiffness of a membrane under low tension.