The present work concerns the numerical modeling of noise and vibration reduction of thin radiating structures in the low frequency range by using shunted piezoelectric elements. The aim is to propose an efficient approach able to predict the most radiating structural modes and to attenuate the corresponding resonances by using piezoelectric patches bonded on the structures and connected to resistive or resonant shunt circuits. The first step is to estimate the sound power radiated by the structure and to determine the vibration modes to be controlled. In a second step, an original finite element formulation, suitable for any elastic structure with surface-mounted piezoelectric patches, is proposed to solve the electromechanical problem. Finally, numerical examples are presented in order to validate and analyze the proposed approach.