A uniform formulation of the effective stress tensor symmetrization procedure has been proposed. This form contains the classical additive and multiplicative symmetrization schemes as particular cases. Different options of symmetrization of the effective stress tensor for the unidirectionally damaged material with parallel microcracks and for the bidirectionally damaged material with a system of orthogonal microcracks were compared. The differences in any forms of the effective stress tensor were second-order infinitesimals for low damage levels. The differences in predictions from considered symmetrization schemes increased with the growth of the damage level and with that of the differences between the eigenvalues of damage. An identification procedure for anisotropic damage was proposed on the basis of acoustic emission methods and then it was discussed.