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The paper is related to the assessment of collapse mechanisms of historic masonry structures suffering settlements induced by ground movements. Two numerical strategies are adopted in order to study the influence of the settled zone on the cracking of masonry buildings: a discrete rigid block model and a continuous homogenized model. The first approach provides an estimate of the collapse load and failure pattern of masonry based on the lower bound theorem of limit analysis. The second approach is formulated in the framework of multi-surface plasticity and implemented in a FE code for the path-following non-linear analysis of masonry wall described as continuous anisotropic plate. Several settlement configurations, of masonry walls under moving ground support are investigated and the corresponding failure patterns resulting from the analysis are obtained resulting in local or global failure modes. The results of the two modeling formulations are compared and discussed in order to highlight the features of the two different approaches in the prediction of settlement-induced damage.