The mathematical models of nanomaterials with triple porosity represent a new possibility for the study of important problems of engineering, technology and mechanics. In nanomaterials with triple porosity, the presence of pores on the following three different scales is considered: (i) macroscale (pore diameter is in the range of 50–1000 nm), (ii) mesoscale (pore diameter is in the range of 2–50 nm), and (iii) microscale (pore diameter is less than 2 nm). Prediction of mechanical properties of nanoporous materials is one of the current topics of continuum mechanics. A comprehensive review of the basic results in the theories for multi-porosity materials may be found in the book by Svanadze [1]. On the other hand, the boundary integral equation method (BIEM) is an elegant mathematical way of transforming boundary value problems (BVPs) of partial differential equations into boundary integral equations. After which the numerical solutions of the BVPs can be obtained using the boundary element method. In the present work, the linear model of thermoelasticity for nanomaterials with triple porosity is considered in which the coupled phenomenon of the concepts of Darcy's law and the volume fraction of pore network is proposed (for details, see [2]). The fundamental solution of the system of steady vibration equations is constructed explicitly. Green’s identities are obtained and the uniqueness theorems for the classical solutions of the basic internal and external BVPs are proved. The surface and volume potentials are constructed and the basic properties of these potentials are established. The BVPs are reduced to the equivalent always solvable singular integral equations for which Noether’s theorems are valid. Finally, the existence theorems for classical solutions of the aforementioned BVPs are proved by means of the BIEM and the theory of singular integral equations. Acknowledgements: This work was supported by Shota Rustaveli National Science Foundation of Georgia (SRNSFG) [Grant # STEM-22-557]. REFERENCES [1] M. Svanadze, Potential Method in Mathematical Theories of Multi-Porosity Media, Switzerland, Springer Inter. Publ. AG, 2019. [2] M. Svanadze, On the coupled linear theory of thermoelasticity for nanomaterials which triple porosity. Mechanics Research Communications, 132, 104161, 2023.