The research of crack-tip field in damage materials is a very complex problem. The core question is how to give the damage constitutive equation and determine the crack tip singularity order of magnitude of the physical quantities. Taking into account the damage process is a process which the energy (strain) accumulates, and the initial damage threshold value existence, on the Lemaitre’s research foundation, the brittle material damage constitutive equation that has the initial damage quantity and the power order relationship with strain is given. Under the assumption that stress (strain) is finite, the construction of III mode crack tip damage fields is studied and the solution of crack-tip stress (strain) asymptotic field is given. Finally, the relationship of the initial crack tip damage zone and full damage zone Scale and material parameters are discusses. These works provide theoretical basis for the material engineering design and the appraisal structure reliability.