Dynamic amplification of loads in masonry arch railway bridges is not well understood. There is a scarcity of experimental data and previous numerical studies have only addressed a few specific bridge geometries. Despite this, guidance documents provide empirical and unvalidated formulae to calculate dynamic amplification for masonry arch railway bridges. To improve our fundamental understanding of the problem, determine appropriate modelling strategies and evaluate the reliability of guidance documents, simple 2D and 3D models are explored in this paper. The 2D approach idealises key bridge components (pier, arch, fill and backing elements) with straight Timoshenko beams, springs and lumped masses. It uses an analytical dynamic stiffness formulation, which is computationally efficient and well-suited to explore a range of bridge models. The higher fidelity 3D modelling approach uses shell and solid finite elements and is used to evaluate the limitations of 2D models. In both approaches, linear-elastic material behaviour is assumed and train loads are idealised as moving vertical loads distributed over an effective area. The modelling results indicate a complex relationship between train speed and dynamic amplification that depends critically on bridge geometry and axle spacing. In general, the multi-span bridge configurations experienced higher dynamic amplification over operational train speeds. The results also higlight deficiencies in existing code provisions and demonstrates how efficient numerical models may replace these provisions.