This paper investigates the dynamic characteristics of a multilevel structure for the transportation and storage of spent nuclear fuel (SNF) from commercial power plants. The nuclear fuel is stored in slender rods that are grouped together into fuel assemblies (FA). In a sealed cylindrical container called “canister”, the FA are inserted into a honeycomb basket. The objective of this paper is to develop a computational model that accurately represents the structural dynamics of the canister as seen from its external surface, such that this computational model can be used in the context of structural integrity assessment of the internal components (FA and fuel rods) based on external vibration measurements. The numerous components lead to a large finite element model, and correspondingly, vibration modes and eigenfrequencies. Nevertheless, the localized connections between components enable an efficient domain decomposition with few interface coordinates. Craig–Bampton (CB) substructuring is thus used to perform the modal analysis. However, the high modal density yields a large-scale CB eigenvalue problem that necessitates a sparse solver. A block factorization by Schur complement that exploits the sparsity of the CB matrices allows an efficient calculation of the numerous eigenpairs. Many local vibration modes contribute little to the dynamics of the SNF canister. The main contribution of this paper is the development of an efficient methodology for determining the importance of each of the substructural modes of the CB model. The removal of the least dominant substructural modes allows for reducing the CB model. Using a 75% filtering, a significant speed-up is obtained, without noticeable loss of accuracy.