A boundary method is applied to study the scattering and diffraction of elastic waves by three-dimensional surface irregularities on the surface of a half-space. The method makes use of the c-completeness of a family of wave functions in order to construct with linear combinations the diffracted fields. Boundary conditions are satisfied in a least-squares sense. For axisymmetric scatterers, an azimuthal decompositon is presented. Some numerical results for vertical incidence of P waves are reported.