The prediction of local failure mechanisms in historical masonry structures and the evaluation of strengthening interventions is a key issue in the protection of built cultural heritage against natural hazards. In recent years, different modeling approaches and software tools were developed for computational analysis of local failure mechanisms via rigid block modeling [1–3]. In these approaches, structures are schematized as an assemblage of rigid blocks interacting at interfaces. Generally, a no-tension frictional behavior is assumed at the interfaces. Different analysis types have been implemented, including limit analysis, nonlinear static and time-history analysis. Actions considered include seismic loads and settlements. In order to consider the effects of settlements on the capacity to lateral loads, support movements and seismic-induced lateral loads can be applied in sequence as well. The numerical problems associated to the different analysis types are formulated and solved adopting a variational-based approach. In this paper, an overview of the integrated variational formulation adopted for the different analysis types is provided along with developed tools for numerical analysis. Potentialities of developed formulations and tools are discussed with applications to experimental and numerical case studies from the literature.