The Thesis presents some numerical models based on homogenization for masonry structures subjected to in- and out-of-plane loads. Joints and bricks are assumed either linear elastic or rigid perfectly-plastic. In the latter case, a simple optimization problem is derived at a cell level to evaluate the macroscopic strength domain of masonry, using both the static and the kinematic theorem of limit analysis. A simple polynomial expansion of the micro-stress field in a finite number of rectangular sub-domains is proposed, suitable to obtain with a very limited computational effort a lower bound...