The concepts of deformation and destruction of materials at different structural levels are presented sequentially. A number of characteristic mechanico-mathematical models of elastic, plastically deforming, and viscoelastic materials are considered. The basic principles of modeling the transition between the individual structural levels of the material are given. Elements of fracture mechanics, modeling of the mechanical behavior of anisotropic materials, etc. are also included. Some results from the authors' own research in the field of mechanics of anisotropic materials and flexible composites are also presented here.