In this paper, we employed the rigorous mode-matching method to carry out the calculation for the scattering characteristics of a two-dimensionally periodic structure made up of metallic rectangular cylinders. From the scattering characteristics, the interesting phenomenon of an anomalous dispersion was observed to possess negative group velocities. In order to understand the underlying physics involved, we begin with the investigation of the band structure associated with the corresponding structure of infinite extent; thereby, the band structures are classified into two types: vertical stop band that is mainly due to the effect of periodicity in a single direction and slanted stop band that is due to the combined effects of periodicities in two directions. Notably, the negative group velocity (delay) within the slanted stop band of a two-dimensional periodic structure was directly related to the experimentally measurable scattering characteristics of the finite structure.