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In the monograph non-classical models of the some Theory of boundary value problems are considered. Basic concepts of dynamic problems of deformable solid elastic bodies of the generalized Green-Lindsay theories of couple-stress thermo-elasticity and couple-stress thermo-diffusion for isotropic, homogeneous elastic media are study . There is worked out the general theory of solvability of dynamical problems for conjugated system of differential equations of thermo-piezoelasticity, formulated by Toupin Mindlin, the diffusion models of linear theory of a two-component elastic mixture using the methods the Laplace integral transform, potential method and singular integral equations. effective solution of boundary value problems for a half-plane are constructed. They are solved explicitly by using the Fourier s integrals. Approximate solution of some mixed boundary value problems for finite domain, bounded by the some closed surface are constructed. They are solved explicitly by using the generalized Fourier's series method.