An exact solution is given for the reflection of a plane wave normally incident on a rigid solid with periodically spaced semi‐infinite circular holes. Analytical considerations, verified by numerical calculations, show that the reflection coefficient is unity at the cutoff frequencies defined by the periodicity of the holes. This result is independent of the volume fraction of the holes. It implies that the porous solid acts like a rigid solid at these frequencies. The problem of plane‐wave incidence from the holes is also solved. A reflection coefficient of unity is obtained at the same frequencies, again implying a rigid effect. Below the first cutoff frequency, the reflection coefficient can be parametrized by a simple scalar frequency dependent quantity. This simple result can be interpreted in terms of a displaced pressure continuity condition.