A Non-Smooth Contact Dynamic (NSCD) formulation is used to analyze complex assemblies of rigid blocks, representative of real masonry structures. A model of associative friction sliding is proposed, expressed through a Differential Variational Inequality (DVI) formulation, relying upon the theory of Measure Differential Inclusion (MDI). A regularization is used in order to select a unique solution and to avoid problems of indeterminacy in redundant contacts. This approach, complemented with an optimized collision detection algorithm for convex contacts, results to be reliable for dynamic analyses of masonry structures under static and dynamic loads. The approach is comprehensive, since we implement a custom NSCD simulator based on the Project Chrono C++ framework, and we design custom tools for pre- and post-processing through a user-friendly parametric design software. Representative examples confirm that the method can handle 3-D complex structures, as typically are architectural masonry constructions, under both static and dynamic loading.