A continuum model for assessing the ultimate failure of masonry as a homogenized material is presented in this paper. It is shown in particular how a homogenization technique implemented within the framework of the yield design theory, makes it possible to construct a macroscopic strength criterion for masonry described as a regular assemblage of bricks separated by joint interfaces. Making use of the kinematic definition of such a criterion which involves velocity jumps across the joints, the yield strength domain in the space of stresses is explicitly determined in the case of infinitely resistant bricks. It clearly shows the anisotropic characteristics of the equivalent medium, due to the preferential orientations of joints. This formulation is particularly interesting from an engineering point of view, since only a few easy to identify parameters relating to the joint strength characteristics (reduced here to a friction angle and a cohesion), and to the brick geometry are involved. As an illustrative application of the criterion so obtained, the stability of masonry walls subjected to inclined gravity loads is investigated by means of the upper-bound kinematic approach. Even though the theoretical predictions derived from this analysis are in good qualitative agreement with available experimental data, the comparison points to the necessary extension of such an approach for taking “scale effects” into account.