Based on the Bloch theory and the flexural wave propagation theorem, the model for calculating the vibration response, sound radiation power and radiation efficiency of an acoustic metamaterial plate is established. The modal analysis of a bare pate and the plate attached to periodical lateral local resonators are developed to investigate the vibration regulation. In addition, the patterns of the sound radiation power and radiation efficiency of the plate attached to periodical lateral local resonators versus frequency are studied. The results show that 1) in a specific frequency range, the mean square velocity and the sound radiation power are far lower than those of the bare plate, which is due to the resonance of the lateral local resonator; 2) unlike the vibration response and sound radiation power, the radiation efficiency of the plate attached to periodical lateral local resonator is higher than that of the bare plate. The investigation of the plate attached to lateral local resonator in this paper lays a solid foundation for the practical engineering in the field of vibration suppression and noise reduction.