The assessment of the internal structural integrity of dry storage casks for used high burnup nuclear fuel assemblies is of critical importance before these are transported to permanent repositories. The size of the casks (5.2 m in height and 2.4 m in diameter), structural complexity and the inability to access the interior make this a challenging task. This project addresses these difficulties through a multi-modal approach involving nuclear, charged particle and acoustic methods. This paper reports on linear and nonlinear vibrational spectra of an unloaded full-scale TN-32 cask. These studies use both impulsive and swept continuous-wave excitations with a variety of sensor placement and cask configurations. From the resulting spectra, resonant frequencies, quality factors and harmonic responses of various vibrational modes were determined. A detailed finite element model of the TN-32 was constructed and the experimental results are compared to the modal structure determined numerically.