We present here a novel numerical method for the upper bound limit analysis of masonry structures. For a given construction, a continuum model composed of planar elements is defined. By assuming a rigid-plastic behaviour, the element kinematics can be decomposed into a rigid body motion and a plastic strain rate contribution. Rigid body velocities and plastic strain rates are the unknowns in the limit analysis problem. Homogenization is followed to represent the actual behaviour of the heterogeneous masonry material. By idealizing masonry as an assemblage of infinitely rigid blocks (bricks) and frictional zero-thickness interfaces (mortar joints), an associative flow rule is derived as a function of the plastic strain rates for use in the continuum model. The limit analysis problem can be so expressed as a linear programming problem which provides, with reference to a variable load condition, an upper bound of the load bearing capacity together with the global velocity field representing the mechanism. Adaptive mesh refinement is finally applied to refine the mesh on the regions where plastic strain rates are detected, minimizing the intrinsic overestimation in the load factor. This approach seems advantageous in comparison with meta-heuristic mesh adaptation schemes already used in the limit analysis of masonry structures. A numerical application on a masonry façade is shown to demonstrate the potential of the method.