Abstract: A fracture model for damaged materials like concrete and rocks is presented in the paper. Based on the process of microcracking from the initiation, stable growth to unstable growth of microcracks, the formation of main cracks and their further development are studied, and the corresponding constitutive relations of the damaged medium and fracture propagation criteria are established. Finally, the proposed fracture model is checked by a geomechanics model test and applied to the feasibility study of a dam foundation with jointed rock mass.