The OSS (acronym of the Italian “Osservatorio Sismico delle Strutture”) is a network of permanent seismic monitoring systems installed on about 150 buildings in Italy. Each system consists of a number of sensors sufficient to completely describe the dynamic response of the structure. Structural typologies have been selected according to their representativeness of the public building stock and to their importance for emergency management. Data available for each building include: structural survey and in situ tests on materials, experimental modal analysis, finite element models and model updating. In the above framework, a school building located in Amatrice, a small town in the meizoseismal area heavily impacted by the 2016 Central Italy earthquake, is one of the buildings instrumented by the OSS; thus, its monitored dynamic response, including that under the main shock, is available. The building showed diffused huge damage with partial collapses. Firstly, a linear finite element model is used in the interpretation of small amplitude vibrations in order to give a reliable dynamic characterization of the initial conditions of the structure. Some relevant quantities of the recorded structural motion under seismic excitation are used to describe the experimental dynamic behaviour. The recorded displacements are then applied to a nonlinear finite element model, and the numerical results are compared with the experimental evidence. The main aim is to discuss the capability of the combined use of experimental response and computational tools in quantifying damage suffered by a structure on the basis of the measured response to an earthquake.