Abstract: An Optimality Criteria is proposed to achieve the optimal placement for constrained damping material in structures. The topology optimization model is presented in which modal damping ratio is designed as an objective function, while constrained damping material consumption is considered as a constraint. The sensitivity of modal damping ratio to damping cell element is analyzed and derived. Furthermore, the formula is used to delete or keep damping cell elements in structures. The numerical examples are demonstrated to verify the effectiveness of the proposed optimality criteria and topology optimization method. The optimal placement of constrained damping material in structures is obtained. The obtained results show the validity of the proposed topology optimization Therefore, a potential application is demonstrated in vibration and noise control of damping structures as a new technical approach.