In the present paper,the uniqueness of the solution to the initialboundary value problem of the linear thermo-elastic dynamics on unbounded do-mains is obtained under less restrictive conditions,including abandoning the positivesemi-definiteness of the elasticity tensor and boundness of the material tensor andrestrictions on the acoustic tensor and the coupled tensor,and the results in[1]arerefined.The conclusion here is valid for the case on bounded domains and the lin-ear elastic dynamics on unbounded domains,hence the results in[2～4]are refinedtoo.Abandoning the positive semi-definiteness of elasticity tensor permits that theuniqueness of the kinetic process is still valid for deformation of the wider materi-als,especially for the case that there are phase-transition during deformation processprovided that the constitutive equations are unchanged in forms.
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