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This paper concerns with the coupled linear dynamical theory of elasticity for solids with double porosity. Basic properties of plane harmonic waves are established. Radiation conditions of regular vectors are given. Basic internal and external boundary value problems (BVPs) of steady vibrations are formulated, and finally, uniqueness theorems for regular (classical) solutions of these BVPs are proved

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In this paper we consider the linear equilibrium theory of thermoelasticity with microtemperatures and some basic results of the classical theories of elasticity and thermoelasticity are generalized. The Green's formulae in the considered theory are obtained. The uniqueness theorems of the internal and external basic boundary value problems (BVPs) are proved. The representation of Galerkin type solution is obtained and the completeness of this solution is established. The formulae of integral representations of regular vector and regular (classical) solutions are obtained. The basic properties of thermoelastopotentials and singular integral operators are presented. Finally, the existence theorems for the internal and external basic BVPs are proved by means of the potential method and the theory of singular integral equations.