Abstract: According to the topological optimization idea, an artificial material hypothesis was proposed, the topological optimization mathematical model of damping materials distribution was constructed. Based on the optimization distribution of damping material, the vibration and acoustic radiation were reduced, in which the mass of the damping material was defined as a constrain condition. By introducing genetic algorithm, the optimization problems were solved, and the structural material conversion between damping material and artificial material was carried out, and the topology optimization of damping material distribution was achieved. Numerical results show that the proposed optimization approach for reducing vibration and acoustic radiation is effective and feasible. The results turn out to have good practicable value in engineering. An feasible and effective method to solve the problem for damping material distribution was provided.