In this study, a system of discontinuous rigid blocks is employed to simulate the possible damage mechanisms in unreinforced masonry (URM) façades and load-bearing frame systems subjected to settlement using the discrete element method (DEM). First, the employed modeling strategy is validated utilizing the available experimental results presented in the literature. Once there is a good agreement between the computational models and experimental findings, a sensitivity analysis is performed to quantify the influence of the input parameters defined in the DEM-based numerical model. Finally, the proposed modeling strategy is further utilized to assess the damage pattern that may develop in a URM façade due to uniform and non-uniform settlement profiles. The results of this study clearly show that the discrete rigid block analysis (D-RBA) provides robust numerical solutions that can be employed to visualize and assess the possible damage patterns and related collapse mechanisms of URM masonry systems as an alternative modeling strategy to standard continuum-based solutions.