Superconducting magnets have complex structures. The coil pack is made up of alternate layers of superconductor and insulator, which form an extremely unisotropic composite structure. For example, the MFTF magnet design, the transverse stiffness is quite soft as compared to the circumferential stiffness [1]. In this study, cylindrically wound superconducting magnets were modeled by two-dimensional multi-rings connected by soft springs, and the internal vibration and buckling of the system were studied both experimentally and analytically. Since the linear elastic theory used in the previous studies [2,3] has failed to predict buckling and vibration of internal turns in the bending mode, elastic ring theory was used in this study. A model based on ring theory and magnetic stiffness was developed to explain experimental observations and showed a fair to good agreement between experimental and theoretical values of the buckling current.