Purpose <p>Locally resonant acoustic metamaterials (LRAMs) can achieve sound transmission loss (STL) beyond the mass law through locally resonant band-gap effects. Conventional LRAM design approaches require repeated geometric modification when the STL peak does not coincide with the target frequency, resulting in manual redesign. This study proposes an inverse design method for determining LRAM geometries that maximize STL at prescribed target frequencies without manual redesign.</p> Methods <p>The proposed method focuses on a manufacturable LRAM configuration consisting of a uniform plate with attached concentrated masses. STL is evaluated using a transfer-matrix-based analytical formulation derived from structural analysis, eliminating the need for acoustic–structure coupled simulations during optimization. Topology optimization is performed using the effective mass parameter of the transfer matrix as the objective function. An extended formulation for multiple target frequencies is also developed. Numerical optimization is conducted for unit-cell models with symmetric boundary conditions.</p> Results <p>The optimization successfully generates geometries that maximize STL at the prescribed target frequencies without manual redesign. The proposed multi-frequency formulation enables the design of LRAMs targeting multiple frequencies. Although some dependence on the initial design field is observed, the shape selection process can be reduced to objective function values and binarization quality. Furthermore, the sharpness of the STL response can be estimated from the evolution of the objective function and volume fraction during optimization.</p> Conclusion <p>The proposed inverse design framework provides an efficient approach for designing manufacturable LRAMs with enhanced STL at specified frequencies. The results demonstrate the feasibility of topology-optimization-based LRAM design without manual geometric tuning and show the potential of the method for practical sound insulation applications.</p>