The aim of the present research was to provide a practical theoretical model based on elementary statics, for assessment for masonry arch bridges, that benefits from the large scale experimental programme at Salford University, together with insight gained from the Distinct Element numerical modelling work. The need for large scale laboratory controlled load tests of physical models that may be reliably confined to a specific domain of behaviour with known parameters and modelling constraints, was highlighted in chapter 2 with reference to literature. Load tests on various distributions of surcharge were carried and the mechanisms of failure observed. The numerical modelled was shown to agree with expected theoretical behaviour and shown good agreement with experimental results. A theoretical model was developed which benefitted from insight from the experimental and numerical work to provide a means of predicting the failure load of the arch-fill system for the lading arrangements carried out in the physical and numerical tests. The model provided predicted failure loads for a range of material variation within a reasonable expected range and showed promising resemblance to the physical modelling results.