Masonry arch bridges often include multiple spans, where adjacent arches and piers interact with each other giving rise to a complex response under traffic loading. Thus, the assumption commonly used in practical assessment that multi-span masonry viaducts behave as a series of independent single-span structures, may not be realistic for many configurations. While several experimental and numerical studies have been conducted to investigate single-span masonry arches and bridges,only limited research has been devoted to the analysis of the response of multi-span masonry bridges. This study investigates numerically masonry arch bridges with multiple spans subjected to vertical loading. For this purpose, an advanced finite element description,which is based upon a mesoscale representation for masonry and accounts for both material and geometric nonlinearities, is employed to shed some light on the actual behaviour of these structural systems. A validation study is first carried out to confirm that the adopted modelling strategy is capable to accurately simulate previous experimental results.Then, the influence of some critical geometrical and mechanical parameters that affect the bridge response is evaluated through a parametric study.The effects of pier settlements and brickwork defects are also investigated, as well as the interaction between adjacent spans through comparisons against the response of single-span counterparts.