Abstract: Elastic wave metamaterials are a class of composite structures/materials constructed from arrayed artificial microstructural units, exhibiting extraordinary physical properties not found in traditional materials. These extraordinary properties are primarily determined by the microstructural cells (local resonant units). For metamaterial beams, they can be classified into force-type resonator, moment-type resonator, and force-moment-type resonator metamaterial beams based on the interaction forces between the local resonant units and the host beam. Currently, most research focuses on force-type resonators, while there is still a lack of in-depth understanding of the bandgap characteristics and mechanisms of force-moment-type resonator metamaterial beams. Based on this, this paper constructs a force-moment-type resonator using a cantilever beam to investigate the band structure and bandgap properties of force-moment-type resonator metamaterial beams. When the beam-type resonators are symmetric, they can be equivalent to decoupled force-moment-type resonators, and the specific parameter relationships between them are established. Simultaneously, an approximate prediction formula for the local resonance bandgap is derived. For asymmetrically arranged beam-type resonators, they behave as coupled force-moment-type resonators. By introducing an asymmetry factor, the influence of coupling effects on the band structure and bandgaps is systematically studied, and phenomena such as bandgap transformation and bandgap coupling are revealed. This study deepens the understanding of force-moment-type resonator metamaterials and provides theoretical guidance for the optimal design and engineering applications of metamaterial beams.