A plane-wave expansion method has been developed to investigate the off-plane propagation of electromagnetic waves in a two-dimensional (2D) photonic crystal. Photonic band-structure calculations indicate that some 2D crystal structures can support a common band gap for both polarizations and for all off-plane angles from $0\ifmmode^\circ\else\textdegree\fi{}$ up to $90\ifmmode^\circ\else\textdegree\fi{}.$ The presence of such an omnidirectional absolute band gap implies that a 2D photonic crystal can exhibit some of the functionalities of a three-dimensional crystal with a complete band gap.
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