This paper presents a constitutive model to describe the non-linear mechanical response of masonry. This heterogeneous material is represented by a fictitious homogeneous medium whose natural basis is defined by the material texture, i.e. its joint planes. The model takes into account the elastic orthotropy of the material as well as the main degradation mechanisms: damage and friction. This thermodynamics-based model is used to estimate the dissipations. This model is implemented in a finite element code and validated at the Gauss point scale. It is then used to evaluate the response of structures subjected to monotonic and cyclic multi-directional loading. An analysis of regularisation methods (energetic and non-local integral) is proposed. This model provides a reliable representation of the overall behaviour of masonry, with the possibility of studying dissipative mechanisms independently.