A formulation for anisotropic damage is established in the framework of the principle of strain equivalence. The damage variable is still related to the surface density of microcracks and microvoids, and, as its evolution is governed by the plastic strain, it is represented by a second-order tensor and is orthotropic. The coupling of damage with elasticity is expressed in tensor form on the deviatoric part of the stress tensor and in scalar form by its trace on the hydrostatic part. The kinetic law of damage evolution is anextension of the isotropic case. Here the principal components of the damage rate tensor are proportional to the absolute value of the principal components of the plastic strain rate tensor The proposed damage evolution law does not introduce any other material parameter Several series of experiments give a good validation of this theory.