The assessment of the seismic response of historical masonry buildings represents a subject of considerable importance but, at the same time, of very difficult task. Refined finite element numerical models, able to predict the non-linear dynamic mechanical behavior and the degradation of the masonry media, require sophisticated constitutive law and a huge computational cost that makes these methods nowadays not suitable for practical application.

In the past many authors developed simplified or alternative methodologies that, with a reduced computational effort, should be able to provide numerical results that can be considered sufficiently accurate for engineering practice purposes. However most of these methods are based on simplified hypotheses that make these approaches inappropriate for monumental buildings.

In this work a three dimensional discrete element model, able to predict the nonlinear behaviour of masonry elements also in presence of curved geometry, is presented. The proposed approach represents an extension of a previously introduced plane and spatial discrete-element conceived for the simulation of both the in-plane and the out-of-plane behavior of masonry historical buildings. The new macro-element enriches a larger computational framework, based on macro-element approach, devoted to the numerical simulation of the seismic behaviour of monumental masonry structures.