Abstract: Analysis and design of the acoustic structure arestudied in the present paper. The sound pressure on a prescribed referenceplane/domain in the acoustic field that is generated by the vibratingstructure is minimized by two-phase damping material distributionoptimization over the structural domain. The Finite element method-Boundaryelement method (FEM-BEM) based structural-acoustic coupling topologyoptimization model is established. The sensitivities of the couplingvariables with respect to the design variables are derived by using thedirect differentiation method as well as the adjoint method. It is pointedout that the adjoint method provides the more efficient formulation forsensitivity analysis when the amount of the reference field points on thereference surface for sound pressure calculation is much less than the totalamount of the design variables. The proposed methods are validated bynumerical examples of the designs of the traveling wave tube and the motorcover. Some interesting features on optimum topologies obtained from thestructural-acoustic coupling designs are revealed and discussed.