Abstract: This paper deals with the damage fracture analysis of mode Ⅲ crack of concrete.Using the theory of damage mechanics, the damage fields near the tip of the crack with static and dynamic loading are derived. In addition, a fracture criterion is developed by means of the concept of damage scale, so that the damage and fracture could be coupled in the same model.The present theory provides a new way to analyze the fracture of concrete crack using damage mechanics.