Detailed modelling of masonry arch bridges and viaducts presents unique computational challenges. Not only do such structures exhibit complex nonlinear behaviour, but they are also difficult to describe within a consistent computational framework for high-fidelity simulations, due to the range of interactive components with varying geometric characteristics. This paper presents a novel parametric model design tool for the generation of detailed 3D FE meshes of realistic masonry arch bridges and viaducts. This tool has been developed according to a modular description as an add-on component within the Rhino – Grasshopper environment. It allows for modular complex bridge assemblages with independent definition of the key viaduct parts, including arch barrels, spandrel walls, piers as well as multi-layered fill. Moreover, new parts can be seamlessly introduced into the framework due to its modular nature. Notably, as all components are geometrically addressable, it is possible to further enhance the model generation tool by adding non-standard routines to create more complex geometry than that allowed by the current parametric definition. Importantly, the developed strategy enables variable fidelity model generation, where different segments of an analysed viaduct can be represented by meso‑ and/or macro-scale masonry descriptions at different levels of detail. This approach further enables the consideration of initial damage in the brick/blockwork, which is a very common feature of many existing masonry bridges and viaducts.