The analytical and algebraic aspects associated with the modelling of reflection–transmission processes for acoustic and electromagnetic waves are investigated. The standard approaches are shown to reduce to selecting m/2 elementary (plane homogeneous or inhomogeneous) waves, among the m available ones, as the generators of the outgoing waves in each half-space. The selection of the generators is performed through the direction of the wave as indicated by the corresponding energy flux. Yet two alternative nonequivalent sets of generators occur for reflected and transmitted waves. This results in two alternative models for the reflection–transmission problem. A detailed comparison of the two schemes indicates that the generators associated with the elementary waves are the only ones which are admissible on a physical ground.