The striking tiled domes of the Ballet School of the Instituto Superior de Arte (ISA) in Havana are internationally acclaimed Cuban architectural icons. However, due to their deceptive tiled appearance and their only recently rediscovered hybrid tile–concrete constructive system, the domes have eluded the structural study and characterization which increasingly is demanded not only because of their unique morphology and monumental status, but also because of their visible damage. This work defined a suitable numerical analysis method for diagnosing these hybrid structures by applying both linear elastic and nonlinear, using the concrete damaged plasticity constitutive model, numerical analyses. A site investigation campaign provided materials and geometric data that informed the model creation and damage documentation that validated the analyses results. A new synthesis of architectural and technical sources covering the development and spread of the hybrid structural system allowed the ISA domes to be placed, for the first time, in their proper structural context and, consequently, for their conception and design to be understood more fully. The analyses, construction records, and site tests indicated a rebar placement error as the primary structural damage cause, and the contextual analysis informed a discussion of its possible sources, both technical and managerial. Because the investigation indicated significant risk of irreversible damage or failure without timely intervention, preliminary intervention explorations were conducted and, based on the holistic understanding of the structures, the technically, architecturally, and culturally optimal solution was identified. The study concluded that the homogeneous solids model, coupled with the concrete damaged plasticity mechanical model, yields realistic and insightful results illuminating the structural behavior, efficiency, condition or status, and collapse mode of the domes, providing necessary insight for the preservation planning for the Ballet School domes, which also will inform the study and understanding of other structures of similar composition and significance.