The vibration analysis of a multilevel spent nuclear fuel canister loaded with 68 fuel assemblies (FA) is considered. The multilevel aspect leads to large numbers of degrees of freedom (DOF) and vibration eigenmodes. The Craig-Bampton (CB) substructuring technique is well suited to perform the modal analysis in presence of few interface DOF between the components and the structural levels, as well as for tackling the high modal density. The Shift-Invert Lanczos solver is used for solving the large-scale CB generalized eigenvalue problem (GEP), whose large dimension results from the numerous component modes. A block factorization based on the Schur complement that exploits the sparsity of the CB matrices enables considerable speed-up. A CB model for the FA is also implemented as it exhibits two structural levels. Since many local vibration modes do not contribute much to the response, a strategy for ranking the importance of the component modes is developed, so that a significant portion of them are removed and the CB GEP lightened.