This thesis describes metamaterials for noise reduction in acoustics and structural dynamics. Through analysis of the unit cell of a 2D periodic metamaterial consisting of the base structure and carefully placed resonating structures, the dynamic characteristics of the whole structure were obtained via dispersion curves. Appropriately sized metamaterials can exhibit band gaps in which free wave propagation is not allowed. Band gaps were identified via dispersion curves which were calculated using a direct and inverse approach. Metamaterial design was also manufactured using FFF 3D printing technique. A good agreement between calculated and measured band gap frequency region was identified. 4 dB stronger noise reduction was measured by metamaterial with a mass ratio of 0.1 between resonators and base structure compared to only its base structure with equivalent mass.