Masonry may be considered macroscopically as a periodic two-phase material. The possible occurrence of cracking in each of the phases leads to a complex mechanical behaviour. Most existing macroscopic models defined for such materials are phenomenological and either isotropic or orthotropic. In this paper, a scalar damage model is used in a mesoscopic study to assess the need for incorporating non-orthotropic induced anisotropy in macrocopic models. Based on unit cell computations and homogenization techniques under a plane stress assumption, it is shown that scalar damage meso-models allow to obtain realistic in-plane damage patterns encountered in experiments. Results suggest that at the meso-scale, it is possible to use a scalar damage model for the individual phases which naturally leads to an overall anisotropy evolution. This evolving macroscopic anisotropy is illustrated using a numerical homogenization procedure to identify the degraded stiffness associated to the obtained damage patterns. It is shown that the characteristic anisotropic shape of experimental failure envelopes for masonry may be reproduced by unit cell computations, as far as in-plane failure mechanisms are concerned.