Vibration characteristics of metamaterial beams manufactured of assemblies of periodic cells with built-in local resonances are presented. Each cell consists of a base structure provided with cavities filled by a viscoelastic membrane that supports a small mass to form a source of local resonance. This class of metamaterial structures exhibits unique band gap behavior extending to very low-frequency ranges. A finite element model (FEM) is developed to predict the modal, frequency response, and band gap characteristics of different configurations of the metamaterial beams. The model is exercised to demonstrate the band gap and mechanical filtering capabilities of this class of metamaterial beams. The predictions of the FEM are validated experimentally when the beams are subjected to excitations ranging between 10 and 5000 Hz. It is observed that there is excellent agreement between the theoretical predictions and the experimental results for plain beams, beams with cavities, and beams with cavities provided with local resonant sources. The obtained results emphasize the potential of the metamaterial beams for providing significant vibration attenuation and exhibiting band gaps extending to low frequencies. Such characteristics indicate that metamaterial beams are more effective in attenuating and filtering low-frequency structural vibrations than plain periodic beams of similar size and weight.