<p>Masonry arches play a crucial role in the seismic response of historic masonry buildings. Although masonry arches are often subjected to large support displacements that alter and deform their geometries over time, their response to seismic actions is generally analysed using idealized, perfect geometries. This paper aims to assess the effect of large support displacements on the response of masonry arches to lateral loads. To this end, a small-scale segmental dry-joint masonry arch subjected to the vertical displacement of one support was investigated. Using a rigid block modelling approach recently proposed in the literature, the arch was modelled as an assemblage of rigid voussoirs connected by no-tension frictional contact interfaces. The response of the arch to lateral loads, applied in one direction, and to vertical support displacements was assessed through nonlinear static analyses. To evaluate the effect of support displacements, lateral loads were applied to a series of deformed arch geometries resulting from the application of increasing values of the imposed vertical displacement. The results of the numerical analyses provided new insights into how support displacements affect the lateral load response of masonry arches, showing that they may significantly reduce both the horizontal action triggering collapse and the ultimate displacement capacity.</p>