This chapter investigates the dispersion relations of metal cylinder-loaded waveguides by leveraging the boundary conditions of periodic structures, which serves as a valuable auxiliary tool for understanding key electromagnetic concepts such as boundary conditions and dispersion relations. Firstly, a research is conducted for the gap waveguide with metal cylinders loaded between parallel plates, their dispersion relations are analytically studied using the boundaryconditions of two-dimensional periodic structures. Further, considering gap waveguides incorporating mutually intersecting periodic short metal pillars, a transmission line model loaded with dual-periodic impedances is established. Based on this model, the corresponding dispersion relation is also derived. Finally, for slot gap waveguides and dielectric-integrated waveguides, a mathematical model describing their dispersion relations is constructed using the transverse resonance method.