A new constitutive model is proposed for the description of induced anisotropic damage in brittle rocks. The formulation of the model is based on relevant results from the micromechanics consideration. The distribution of microcracks is approximated by a second order damage tensor. The effective elastic properties of damaged material are derived from the enthalpy function. The evolution of damage is directly related to the growth of microcracks in different space orientationns. The volumetric dilatancy due to sliding crack opening is taken into account. The model is extended to the description of creep deformation in brittle rocks. The time dependent deformation is seen as a consequence of the sub-critical propagation of microcracks due to stress corrosion process. The proposed model is applied to a typical brittle roc, the Lac du Bonnet granite. A general good agreement is obtained between numerical simulations and experimental data.