The assessment of the internal structural integrity of dry storage casks with high burnup nuclear fuel assemblies is of critical importance for their transport to permanent repositories and during their extended storage service lives. The large size, structural complexity, and inability to access the interiors of the casks make this task challenging. The aim of this work is to evaluate the ability of vibrational characterization to assess the state of the internal cargo (i.e., fuel assemblies) in a cask strictly using measurements on the outer surface. In this study, we report on the identification of five modes of an unloaded full-scale Transnuclear-32 (TN-32) cask and examine the potential of using these modes to assess the internal configuration in a loaded condition. Vibrational spectra were acquired using impulse and continuous-wave techniques on both storage and transportation configurations from which the modal frequencies and the associated quality factors were determined. A finite element model of the TN-32 was constructed and used to identify the observed modes. The model was extended to include loaded configurations to assess how the presence of assemblies impacts the modal structure of the cask and its surface vibrations.