This paper deals with the fully coupled linear theory of thermoelasticity for triple porosity materials. The system of general governing equations of motion is expressed in terms of the displacement vector field, the pressures in the three pore systems (macro-, meso- and micropores) and the temperature. The fundamental solutions are constructed explicitly by means of elementary functions for the five special cases of the equations of motion: (1) equations of steady vibrations; (2) equations in the Laplace transform space; (3) equations of steady vibrations in the quasi-static theory; (4) equations of equilibrium; and (5) equations of steady vibrations for rigid body with triple porosity. Finally, the basic properties of these solutions are established.
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