Masonry arches represent the most important structural components of masonry arch bridges. Their response is strongly affected by material nonlinearity which is associated with the masonry texture. For this reason, the use of mesoscale models, where units and mortar joints are individually represented, enables accurate response predictions under different loading conditions. However, these detailed models can be very computationally demanding and unsuitable for practical assessments of large structures. In this regard, the use of macro-models, based on simplified homogenised continuum representations for masonry, can be preferable as it leads to a drastic reduction of the computational burden. On the other hand, the latter modelling approach requires accurate calibration of the model parameters to correctly allow for masonry bond. In the present paper, a simplified macro-modelling strategy, particularly suitable for nonlinear analysis of multi-ring brick-masonry arches, is proposed and validated. A numerical calibration procedure, based on genetic algorithms, is used to evaluate the macro-model parameters from the results of meso-scale “virtual” tests. The proposed macroscale description and the calibration procedure are applied to simulate the nonlinear behaviour up to collapse of two multi-ring arches previously tested in laboratory and then to predict the response of masonry arches interacting with backfill material. The numerical results confirm the ability of the proposed modelling strategy for masonry arches to predict the actual nonlinear response and complex failure mechanisms, also induced by ring separation, with a reduced computational cost compared to detailed mesoscale models.