(Authors’ summary.) A plane acoustic wave is incident upon an infinite, rough, impenetrable surface \(S\). The aim is to find the scattered field by deriving a boundary integral equation over \(S\), using Green’s theorem and the tree space Green’s function. This requires careful consideration of certain integrals over a large hemisphere of radius \(r\). It is known that these integrals vanish as \(r\to\infty\) if the scattered field satisfies the Sommerfeld radiation condition, but that is not the case here – reflected plane waves must be present. It is shown that the well-known Helmholtz integral equation is not valid in all circumstances. For example, it is not valid when the scattered field includes plane waves propagating away from \(S\) along the axis of the hemisphere. In particular, it is not valid for the simplest possible problem of a plane wave at normal incidence to an infinite flat plane. We discuss some suggestions for modified integral equations.