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The paper reports the results of a research aimed at analyzing and interpreting the cracking pattern on the Cappella dei Principi (Prince's Chapel, the Medici's mausoleum) in the Basilica of San Lorenzo (Florence, Italy). The research was motivated by the sudden collapse of a keystone of an internal barrel vault sustaining one of the lateral apses. After a brief description of the geometry of the structure, the principal results obtained from in situ surveys (flat-jack tests and cored samples) are described; then the numerical analyses developed both to obtain the static identification of the monument and to assess the possible causes leading to the observed failure are illustrated. The numerical modeling operation has been performed step by step, from linear and quite simple models built with plane elements up to a nonlinear model with three-dimensional elements. The nonlinear FEM, which has been tuned by utilizing the results of the in situ measures, is allowed to both qualitatively and quantitatively reproduce the behavior of the structure and its static problems in the area of the barrel vault over the side apses, allowing for justification of the manifested damage. The comprehension of the structural behavior allows identification of a proper retrofitting strategy. [ABSTRACT FROM AUTHOR]