To realize the prediction of strongly coupled sound radiation and the optimization of noise in both internal and external sound fields, the finite element/boundary element coupling equation was established, and two methods for solving the sensitivity of sound power were proposed. First, the coupled finite element equations of the structure and the internal sound field were given. Considering the interaction of the external acoustic medium to the structure, the finite element/boundary element coupling equation was established according to the continuity of interface force and normal velocity. Then, in view of the difficulty of decoupling in element sensitivity analysis in sound power topology optimization, the sound power was converted into an expression with structural displacement as variable, and the adjoint equation was modified to realize the extension of the method to the strongly coupled optimization problem. The direct derivation method of sound power sensitivity was proposed considering the complicated derivation process of the adjoint variable method (AVM). Finally, the linearized stiffness method was adopted, which takes the relative density of structural elements as continuous design variables, and the optimization of different structural materials and acoustic media was studied. Comparison results show that the sound power calculated by the coupled model was consistent with that of the finite element method without reflection boundary. Both direct derivation method and AVM could quickly achieve convergence, but the derivation process of the direct derivation method was more concise and efficient. Numerical optimization proves that the optimization algorithm has good applicability and is effective in sound power optimization design.