A wave composed of weak and short waves (WS waves) in a dynamically deformed elastic material is studied theoretically by using quasigeometrical acoustics. The material considered is one dimensional and inhomogeneous with a nonlinear stress–strain relation. A general theory for analyzing the composite wave is exploited. It is shown to the second‐order approximation that the analysis of the composite wave can essentially be reduced to the analysis of a single WS wave. As an example of the general theory, a head‐on collision between two WS waves is investigated.