The accuracy of the Kirchhoff approximation for randomly rough, pressure‐release surfaces has been examined through comparison with exact numerical results based on solving an integral equation. A Gaussian roughness spectrum was chosen for the surfaces, and a Monte Carlo procedure was used to obtain the average bistatic scattering cross section. Results will be presented that illustrate the breakdown of the Kirchhoff approximation as the incident grazing angle is reduced and as the average radius of curvature is reduced. The accuracy of shadowing corrections to the Kirchhoff approximation will also be discussed. [Work supported by ONR.]