Abstract. Among elastic crystals which are subjected to phase transitions are those which represent so-called ferroic states. These are elastic ferroelectrics, elastic ferromagnets and ferroelastic crystals such as twinned shape-memory materials. In these three wide classes studied by the author and co-workers, the solitary waves which can be shown to exist and represent either moving domain walls or nuclei of transformations, are not true solitons since the interaction of two such waves always is accompanied by some linear radiation. This is a consequence of the very form of the governing systems of equations which may be of different types (e.g., sine-Gordon equation coupled to wave equations, modified Boussinesq equation) and are usually obtained either from a discrete lattice model or a rotationally invariant continuum model. For the sake of illustration the case of shape-memory materials is presented in greater detail through the first approach.