The skeleton theory evolves the structural macroscopic theory, when being applied to the analysis of globally and locally curved filaments. Applying the skeleton theory, we implement a rigorous description of macroscopic behavior of the media of the filament composites under small and large deformations. The theory is based on a concept of skeleton points of a composite material. At that, similarly to the structural macroscopic theory, we combine the analysis at the micro- and macromechanical levels. We combine the micro- and macromechanics of composites using the skeleton field of displacements, which defines location of the skeleton points in a current medium, and a current macroscopic configuration of composite medium. The concept of macroscopic stresses applied allows us to study the composite media under arbitrary deformations of structure’s components. The materials of a structure’s components can be described both by elastic models and by models of more general rheological type. The theory can be extended to matrix composites and laminated and hybrid composites with linear and curved structures.