The present paper is devoted to a two-component model of material with nonlinear interaction force, which describes the dynamics of crystalline lattice transformation under shock-wave loading. The governing equations are written for the center of mass displacement and relevant displacement of the components, which is considered to be an internal degree of freedom, responsible for structural transformations. Basing on the analogy between the continuum equations and the corresponding discrete model, we carry out the investigation of the quenching of a non-stationary wave due to the dissipation of energy into structural conversions and estimate the duration of this process. The obtained analytical results are confirmed by the numeric calculations performed by finite difference method.