Masonry-like materials, such as brick-block masonry or rocky materials, are modelled as discrete systems of rigid blocks in dry contact. Compressive and frictional interactions are considered. A computer procedure to determine the collapse load for two and three dimensional structures using a non-standard limit analysis approach is implemented. The mechanisms of hingeing, sliding, and twisting at the block interfaces are accounted for. The solution of the problem of non linear programming, corresponding to limit analysis in the presence of friction at interfaces, is obtained by solving a preliminary problem of linear programming, corresponding to a linearized limit analysis in the presence of dilatancy at the interfaces. Numerical analyses are performed for two and three dimensional systems with many degrees of freedom. The non linear and linearized solutions are compared and discussed. Experimental results are also presented and compared with the numerical solutions.