In this paper, we discuss how to obtain the dispersion characteristic of a periodically loaded waveguide from the band structure of an equivalent unbounded artificial periodic material. We examine the filtering properties of a waveguide that is periodically loaded with metallic disks. Unlike the traditional design (R.E. Collin, Field Theory of Guided Waves, 2nd Ed., IEEE Press, 1991), which is based on lumped-element analysis and optimization (C. Kyriazidou et al, IEEE Trans. on MTT, vol. 49, pp. 297, 2001), our analysis is full-wave. This allows us to investigate the filtering properties of structures in which the distance between the disk-planes is small, and to take into account the granularity of the transversal lattice. We discuss how the number of elements in the cross-section of the waveguide and the permittivity of the host material, influence the band-gap width and position. We study in addition the effect of transversal off-setting adjacent disk-planes. The theoretical results are validated against experimental data.