Predicting the structural response of masonry structures with acceptable accuracy is paramount to safeguard the historical heritage and build new constructions with safety margins adequate to modern standards. However, due to the heterogeneous nature and anisotropic response of masonry, such prediction is still difficult to achieve, where most current masonry representations are based upon homogeneous isotropic material models or even more simplified masonry macro-elements. In this article, a novel anisotropic constitutive model to be used in detailed 3D continuum FE representations is described. This is based upon the application of the transformed-tensor method to an isotropic uncoupled plastic-damage model, which is further enhanced by additional novel features enabling the proper definition of the shear behavior both in terms of yielding surface and damage evolution while increasing local computational robustness. Illustrative examples at different scales are presented, highlighting the characteristics and potential of the developed masonry material model. Focus is placed on the mechanical behavior under uniaxial and biaxial stress states considering pure compression on wallets with varying inclination of the material principal axes and the out-of-plane response of wall components. The numerical results confirm the ability of the proposed constitutive model to predict typical masonry anisotropic response characteristics, which cannot be accurately represented by standard isotropic representations commonly used in professional practice and research.