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Masonry arch bridges are often between 100–150 years old and have complex histories of damage. Uncertainties regarding their condition and behaviour can present asset management challenges, potentially leading to operational restrictions that may or may not be warranted. This can be compounded when the extent, severity, and cause of deformations are difficult to judge. The challenge is particularly onerous for skewed arch bridges, which can behave highly three-dimensionally. Point cloud-based analysis offers a means to interrogate long-term structural deformation and can be coupled with theories of masonry behaviour to interpret kinematic mechanisms behind these movements. Building on previous work by some of the authors, this paper utilises exploratory point cloud-based assessment to study two typical skewed arch bridges. Specifically, the methodology enables distributed structural deformations to be mapped relative to best-fit shapes representing likely construction geometry, and for kinematic mechanisms to be overlaid on these maps. In this way, potential magnitudes of support movements behind the observed deformations may be gauged. The two case studies highlight the complex three-dimensional behaviour of skewed masonry bridges and provide experimental evidence of concentrated support deformations at their obtuse corners, aligned with their square span direction. This is consistent with the hypothesis that large thrusts may initially follow the square span direction before being redistributed as local deformation of these corners occurs and that, consequently, assumptions of rigid boundary conditions for skewed arch bridges are unrealistic. • Concentrated deformation is observed at the obtuse corners of historic skewed arches. • Kinematic arch mechanisms are visualised and associated support movements quantified. • Large initial thrusts aligned with the square span may have led to redistribution. • Assumptions of rigid boundary conditions for skewed arches are therefore unrealistic. • The MATLAB app that enabled this point cloud-based analysis has been made available.