Based on analysis of deformation in an infinite isotropic elastic matrix con-taining an embedded elliptic crack, subject to far field triaxial compressive stress, the energy release rate and a mixed fracture criterion are obtained by using an energy bal-ance approach. The additional compliance tensor induced by a single closed elliptic microcrack in a representative volume element and its in-plane growth is derived. The additional compliance tensor induced by the kinked growth of the elliptic microcrack is also obtained. The effect of the microcracks, randomly distributed both in geometric characteristics and orientations, is analyzed with the Taylors scheme by introducing an appropriate probability density function. A micromechanical damage model for rocks and concretes under triaxial compression is obtained and experimentally verified.