The Expected results of the research are formulated as follows:
1. The following six mathematical models will be presented:
 a) The 3D coupled linear mathematical models of elasticity for double and triple porosity materials;
 b) The 3D coupled linear mathematical model of thermoelasticity for double porosity materials;
c) The 3D coupled linear mathematical models of viscoelasticity for single, double and triple porosity materials.
2. In these new models the following problems will investigated:
a) The fundamental solutions of the systems of steady vibration equations will be constructed by elementary
functions and their basic properties will be established;
b) Green’s formulae for the systems of steady vibration equations will be obtained;
c) The uniqueness theorems for classical solutions of the internal and external boundary value problems (BVPs)
of steady vibrations will be proved;
d) The basic properties of surface and volume potentials will be established. The BVPs of steady vibrations will
be reduced to the equivalent singular integral equations;
e) The existence theorems for classical solutions of the internal and external BVPs of steady vibrations will be
proved by using the potential method (the boundary integral equation method) and the theory of singular
integral equations.