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This paper investigates metamaterial functionally graded plates with quasi-zero stiffness resonators. This way, the governing equations of free vibrations and the mode shapes are obtained using the assumed mode method. The free vibrations analysis of the metamaterial functionally graded plates is then performed using finite element analysis. The objective of the current paper is to present an FG metamaterial plate structure to attenuate its mode shapes. Various resonators’ arrangements on the FG plate evaluate the best arrangements. This paper shows that the proposed metamaterial attenuates the corresponding shape modes for the first nine natural frequencies.