Metastructures made of spring-mass resonators present a bandgap at the natural frequency of the resonator. This rule cannot be generalized for more complex resonators. This work analyzes the case of a metastructure composed of a periodic arrangement of vertical beams rigidly joined to a horizontal beam. The vertical beams work as resonators, and their natural frequencies play a strong role on the band structure of the whole system, however, different than the case with spring-mass resonators. Since this metastructure can be considered a lattice, Bloch’s theorem is applied to the unit cell and a numerical procedure based on the finite element method permits to obtain the dispersion curves. Illustrative results show the influence of the natural frequencies of the horizontal and vertical beams on the band structure.