In this work, we present a modeling methodology to solve the eigenvalue problem for periodic structures with a hexagonal lattice. The method is based on the previously proposed multi-modal transfer matrix method, which is a hybrid method that takes into account the coupling between the multiple modes of the ports surrounding the single unit cell. Commercial software can be used to obtain the generalized scattering parameters which are subsequently applied to set up and solve the eigenvalue problem of the periodic structure. This approach has the ability to obtain complex solutions and thus makes it possible to analyze the attenuation in the stopbands. Here, we extend the multimodal transfer matrix method to the efficient solution of the resulting eigenvalue problem for the case of a hexagonal lattice, detailing the selection of the appropriate supercells and the appropriate irreducible Brillouin zones. Two types of structures are analyzed: a mirror-symmetric structure and a glide-symmetric structure. Very good agreement is obtained with commercial software, limited to the real part of the dispersion diagrams.