A general model of generalized linear thermo-viscoelasticity for isotropic material is established taking into consideration the rheological properties of the volume. As special cases the corresponding equations for the coupled thermo-viscoelasticity and the generalized thermo-viscoelasticity with one (Lord-Shulman theory) or with two relaxation times (Green-Lindsay theory) are obtained. The cases of thermo-viscoelasticity ignoring the rheological properties of volume can be obtained from the given model. The equations of the corresponding thermoelasticity theories result from the given model as special cases. A formulation of the boundary integral equation method, fundamental solutions of the corresponding differential equations are obtained and the dynamic reciprocity theorem is derived for this general model. Generalizations of Somiliana’s –Green and Maysels formulas are obtained. An example illustrating the BIE formulation is given. Special emphasis is given to the representation of primary fields, namely temperature and displacement.

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