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. A novel formulation has been proposed for the limit analysis of large three-dimensional masonry block assemblages. The model is based on a 'point-contact' formulation, also known as 'concave contact' formulation according to the definition given by R. K. Livesley, using contact points located at the corners of the interface to represent interactions. The procedure is based on the assumption that at each step of the analysis sliding behaviour is governed by a fictitious failure condition with an associative behaviour, which is updated at each step of the analysis.