The present study aims to investigate how the roughness of the diffracting surface influences the diffraction field for a plane wave incident on this surface. The roughness is modelled by a rapidly oscillating periodic contour described by a function \(\varepsilon F \left( {x \over \varepsilon} \right)\), where \(\varepsilon\) is a small parameter. For the Helmholtz equation, a full asymptotic expansion of the solution is obtained and it is shown that the roughness influence can be taken into account by the variation of the surface impedance. In the particular case of the diffraction of a \(H\)-polarized wave on a cylindrical surface, the asymptotic results are compared to numerical ones.