The one-dimensional non-linear equations governing dilatational thermoelasticity are presented and a rate-type heat flux law is postulated. The charateristic wave speeds are then calculated for those materials possessing a free energy function. Two types of wave are possible: a mainly mechanical wave and a mainly thermal wave. The shock equations are also stated and from them two dilatational shock speeds are determined. The equations displayed in this paper belong to a class of generalised conservation laws for which an evolutionary criterion is constructed. The criterion is then compared with the entropy inequality as a means of rejecting physically unrealistic shock solutions of the equations of thermoelasticity. © 1974 Springer-Verlag.