A Masonry Building Cluster (MBC) is made from an assemblage of buildings and thus has a non-unitary origin: however, under certain conditions, Structural Units (SUs) can be identified and analysed independently. Starting from a deterministic simplified procedure developed by the authors, a fully probabilistic method of analysis of a SU has been developed, which treats as uncertain all relevant variables, such as: general data, geometry, construction details, materials. This allows to perform fully probabilistic Monte-Carlo-based analyses that allow to compute the failure probability of the MBC. The subsequent sensitivity analyses allow in turn to identify the effect of the different variables on the global response. The latter step proved to be very useful to single out the structural elements worth of a deeper investigation, thus reducing the uncertainty of the assessment outcome.