The vibrational behaviour of beam systems can be expressed in terms of waves of both propagating and near field types. A propagating wave incident upon a discontinuity gives rise to reflected and transmitted waves of both kinds whose amplitudes may be found from well-known reflection and transmission coefficients. In this paper the approach is extended to the case of incident near field waves, reflection and transmission matrices being derived for the cases of a point support and a change in section. Reflection at a boundary and the effects of applied excitations are also considered. It is seen that incident near fields can give rise to substantial propagating components. The application of the results to the analysis of free and forced vibration of beams is then demonstrated. By adopting this approach the effects of the interaction of the near fields with neighbouring discontinuities are fully included.