Abstract Locally resonant acoustic metamaterials have recently attracted a great interest due to their dynamic behaviour, characterized by a band gap at relatively low frequencies. This paper provides a numerical study, by means of finite element modal analyses, of the dynamic properties of 1D mass-in-mass and 2D cellular locally resonant metamaterials. The 2D metamaterial is constituted by a cellular metallic lattice, filled by a soft light material with heavy inclusions or resonators. The influence of material parameters and cell geometry on the band gap width and frequency level are explored. In addition to the usual square lattice we also consider a hexagonal one, which proves to be more efficient for wave filtering.