The potential method is extended to treat the reflection and scattering of acoustic waves by rough surfaces. The resulting expression for the scattered pressure contains terms which can be identified as the singly and multiply scattered field components. In addition, a boundary condition that approximately accounts for shadowing is used. Only the singly scattered field term is specialized to a form that is convenient for reflected or scattered pressure and intensity calculations. Finally, the assumption of a randomly rough surface is introduced and very general results concerning the coherent and total scattered fields are obtained.