Masonry has historically been one of the most widely used construction materials. Despite this, there is a lack of computational tools for the analysis of masonry structures compared with what is available for steel and concrete structures. One of the main reasons is likely to be found in the peculiar mechanical behavior of masonry, which shows a small and unpredictable resistance in tension and a nonlinear inelastic behavior in compression. In this paper we put forward a constitutive model for masonry based on the extension to associate path-dependent plasticity of the classical normal, elastic, no-tension model. This new model allows the onset of fracture and irreversible crushing of the material and accounts for a wider variety of stress states within the structure, highlighting the progress of pseudorigid kinematics. The elastoplastic problem is decomposed into a sequence of nonlinear elastic problems formulated in variational form, which are solved by searching for the minimum of a suitable functional via descent methods. The model is implemented in variational finite element code and validated against analytical solutions and experimental tests. Applications to realistic cases are presented showing the capability of the model to reproduce nontrivial cracking and crushing patterns