This paper presents an optimization study of sandwich plates with corrugated cores for minimizing the transmitted sound power, considering the manufacturability of the structure and constraints on the structural weight and fundamental frequency. A two-dimensional plate model is developed based on the spectral element method (SEM) for the calculation of the frequency-domain vibration response of the whole sandwich structure subject to airborne excitation, and the Rayleigh integral formula is used to calculate the transmitted sound power via its structure-born path. A genetic algorithm-based multi-parameter optimization method is employed to search for the optimal structural parameters with the objective to minimize the sound power transmitted. It is indicated that the optimization results depend highly on the properties of resonant modes in the targeted frequency band. Because of the local modes of the sandwich structure in the high frequency band, the transmitted sound power can be significantly reduced with neither increasing the structural weight nor deteriorating the bending stiffness.