An anisotropic damage model is proposed for concrete materials. As required by thermodynamics a single damage variable, tensorial, is considered for any loading: as a state variable it represents the micro-cracking pattern whatever the loading sign. Damage anisotropy is used to model the strong dissymmetry tension/compression.The Ladevèze damage variable H = (1 − D)^−1/2 is introduced within a deviatoric/hydrostatic split. An original shear-bulk coupling is derived, in accordance with numerical discrete element computations. The sought property of gradual stress softening, with a tail in stress–strain diagram, is obtained. Stress triaxiality is used to enhance the performance of Mazars criterion and therefore of the full anisotropic damage model in bicompression.