A finite element method based on upper bound limit analysis is proposed to estimate the collapse acceleration that induces local failure mechanisms in existing masonry structures. The structural assessment follows the Italian building code, with the added flexibility of not relying on predefined failure mechanisms. The structural model is composed of infinitely rigid hexahedron elements interconnected by quadrilateral interfaces, where plastic deformations are concentrated according to a to a failure criterion such as the Mohr-Coulomb model. The limit analysis problem is formulated following the kinematic approach and solved through a well-established linear programming algorithm. This approach allows the automatic detection of the collapse acceleration and the corresponding failure mechanism, depending on the tensile strength. Through an iterative extrapolation procedure, the solution for the no-tension material model is obtained – as required by Italian standards and commonly assumed for masonry structures in the technical literature. The methodology can also account for the presence of tie-rods. Furthermore, an innovative filtering algorithm is introduced to consider only the elements implicated in the failure mechanism, allowing for the evaluation of the collapse spectral acceleration. The methodology is used for the seismic assessment of a portion belonging to complex historical building in Italy.