Abstract Nanoparticles, hyperthin films, nanotubes and composite materials obtained on the base of such nanostructures exhibit very attractive mechanical properties and are great interest to researchers from continuum mechanics. In this paper, we intend to develop the multiscale continuum model of solids to explain the uncommon properties of the thin structures and the composite materials with thin structures associated with special type local interactions between nanoparticles and matrix. We have used the variation approach assuming that the internal interactions are determined by general character of kinematical connections. This approach allows introducing the system of internal interactions of various types consequently, which correspond to various types of kinematic restrictions in the considered mediums. The model of Cosserat’s pseudocontinuum with both non-free deformations, which depend on the other generalized coordinates and free deformations and rotations (continuous field of defects) but with symmetric stress tensor was proposed. The particular model is considered, which according to the authors view may serve as base for investigations of the scale effects due to cohesion interactions. Description of the cohesion field near top of cracks and composite materials with inclusions are considered in this research.