In this study, the application of elastic metamaterial for suppressing flexural vibration of a thin plate structures is investigated. An elastic metamaterial with hexagonal prism inclusion is proposed and through a parametric study, the effect of the design parameters on bandgap properties are presented. It is found that the tuning of the geometrical structure of the elastic metamaterial unit cell can effectively tune the bandgap location to a particular frequency range of interest. In contrast to previous studies that only consider the bandgap property of elastic metamaterial, in this work, the flexural bandgap of the metamaterial that is attached to a thin plate structure is investigated by numerical simulation. It is observed that when it is applied to a thin plate structure, a low frequency flexural bandgap can be formed, and the proper adjustment of the parameters can effectively influence the bandgap properties. This study demonstrates the effectiveness of the proposed elastic metamaterial for flexural vibration control of thin plate structures.