Unreinforced masonry (URM) buildings may be subjected to exceptional loading conditions during their service lifetime. Extreme loads include soil settlements or even local structural failure that can lead to different levels of damage ranging from severe cracking to partial or total collapse. Predicting the structural response of URM buildings to soil settlements is a complex task, due to the inherent complexity of mechanical behaviour across multiple scales (URM assemblage, components, system) as well as the important effects of soil-structure interaction (SSI). In this study, discrete block-based approaches were used into an applied element framework to simulate the response of URM walls subjected to Gaussian settlement distributions. The presence of URM vault thrusts is considered through distributed in-plane and out-of-plane loads, whereas SSI is accounted for by means of nonlinear Winkler springs. Major effects of load redistribution between structural members and the development of complex failure modes are highlighted. These results can then be used as a basis to perform further investigations considering more complex scenarios at structural scale.