Differential settlements have adverse effects on the serviceability and stability of vaulted masonry structures. However, the existing monitoring and assessment techniques do not capture these effects in sufficient detail. In this paper, a new approach is proposed to better describe the influence of support movements on barrel vaults. In this approach, laser scan point clouds of a settling vaulted structure are compared. Different cloud comparison methods are used to accurately identify the displacements of small point cloud segments. In particular, a new cloud comparison method, which modifies the well-known iterative closest point (ICP) registration algorithm, is developed. By constraining ICP to ensure displacement continuity between adjoining point cloud segments, three dimensional movement estimates of the structure are obtained. These estimates delineate the settlement response by indicating the location and magnitude of cracking. This rich information is then used to identify the settlement response mechanism of the vault using limit state numerical analysis. Finally, by interpreting the numerical results with relevant serviceability criteria, a new method to quantify the influence of settlements on barrel vaulted masonry structures is proposed. This damage assessment technique is used to evaluate observed damage due to piling-induced settlements in a masonry viaduct at London Bridge Station.