A substantial part of the underline bridges that belong to the asset collection of the main railway and roadway infrastructure operators in the UK and Europe have the structural shape of arches, typically constructed from brick/stone masonry. Current assessment methods, which consider 2D descriptions for masonry bridges, do not enable an accurate representation of the typical 3D response, and often they do not provide realistic predictions of the development of damage in the various bridge components including arches, piers and spandrel walls. In this paper, two alternative 3D FE modelling strategies offering different balance between sophistication and computational efficiency are presented. The first approach is based upon a detailed mesoscale masonry model, where a distinction is made between constituents allowing for an accurate description of masonry under various bond conditions. Alongside elastic solid elements representing the bricks, nonlinear interface elements are used to model the mortar joints and the potential cracks across the brick bulk. The second approach is based on macroscale representation, where a homogeneous description of masonry is assumed employing elasto-plastic solid elements with damage to represent the masonry components of arch bridges. In both approaches, backfill is modelled by elasto-platic solid elements and the interactions between the spandrel walls and the backfill and arches, as well as between the backfill and the arches’ extrados, are explicitly incorporated to the model. This interaction effect is investigated with the two approaches, and comparisons are made between the respective simulations to illustrate the relative benefits of mesoscale and macroscale modelling.