Masonry arch structures constitute a significant part of the international architectural heritage. Particularly, they play a key role in transportation infrastructures. Despite their ageing and degradation due to environmental effects and evolving operational requirements, many of these bridges continue to remain in service. Ensuring their continuous and safe operation is of critical importance for the adequate performance of road and railway lines. Thus, the ability to monitor their structural health is becoming of increasing interest. In specific, there is a need to identify damage-sensitive features (DSF) that can help maintain serviceability and prevent failures with potentially severe structural and economic consequences. To this aim, this research focuses on a 3D FEM masonry multi-arch model, to which typical damage has been gradually introduced. The modal analysis of the model at different stages of damage serves to identify DSF that can contribute to accurately distinguish between damaged and undamaged states, providing valuable insights for the monitoring of real-life masonry arch structures and to anticipate potentially dangerous damage propagation phenomena. The ultimate aim of the research is found in developing a comprehensive and cost-effective approach to anticipate failure propagation in ageing bridges.