ABSTRACT: A 3D rigid body model is formulated to investigate the behaviour of masonry block structures subjected to foundation settlements. The structural model is an assemblage of rigid blocks which interact at contact interfaces. Contact forces are located at the vertices of interfaces and a no-tension and non-associative frictional behaviour with infinite compressive strength is considered for joints. The limit analysis problem is formulated as a mathematical programming problem and a computer program has been developed for applications of the proposed procedure. The rigid block model has been validated against the results of experimental tests carried out on small scale panels, made of dry-jointed tuff blocks with dimensions of 200 × 100 × 50 mm. The bearing support system was designed so to induce a uniform settlement along a part of the panel. The comparison of numerical and experimental results was carried in terms of failure mechanism and distribution of base reactions at collapse. To evaluate the computational efficiency of the developed formulation, an application to a numerical case study of a 3D building with a large number of blocks and contact interfaces is also presented.