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Reliable numerical analysis strategies for historical unreinforced masonry buildings under seismic action represent essential tools in engineering practice in order to assess their actual resilience and study their vulnerability to earthquakes. In this note, an approach based on the Discrete Element Method is proposed to assess the seismic fragility of stone masonry buildings: stone masonry is regarded as a set of small discrete elements (masonry units) modelled as rigid blocks, while the nonlinear behaviour is limited to that of the joints. A procedure for performing push-over analysis and obtaining the capacity curve is implemented using the software UDEC, and the results are compared to the classical mechanism method. Eventually, the approach is applied to the library of the Casamari Abbey in Veroli (FR, Italy), a Cistercian complex dating back to the XIII century.