The stopband structure of a two‐dimensional periodically corrugated waveguide is investigated by means of the null‐field method. In the numerical examples, the walls are assumed to be hardwalled with symmetric, antisymmetric, or one‐sided sinusoidal corrugations. The interaction pattern and the stopband widths are determined for the lowest modes. The resonances are found to be of the stopband type, and it appears that geometrical symmetries of the boundaries suppress well‐defined sets of resonances.