Abstract: Based on principle of continuum damage mechanics, the mechanical response of the elasto-brittle material with damage is analyzed theoretically in this paper. Both material and damage are considered to be anisotropic. The expressions for the damage tensor, the effective elasticity tensor, the true stress tensor and the damage energy dissipation rate tenare also derived.Based on principle of continuum damage mechanics, the mechanical response of the elasto-brittle material with damage is analyzed theoreticall...