Destruction of geomaterials and geomedia material, as well as general brittle and ductile materials, have been treated theoretically and experimentally using the general approach of nonlinear dynamic systems. The process of destruction in loaded solids (inelastic deformation, damage accumulation, fracture) is presented as a space-time evolution of a nonlinear dynamic system, which allows interpreting all deformation and fracture within the limits of a single theory. The space-time hierarchies of nonlinear systems were found out to undergo collective effects and self-organization. The experimental and theoretical studies of the evolution of loaded solids revealed their universal fractality and showed brittle fracture and plastic deformation to be self-similar processes at different scales, for which scaling parameters have been estimated. The evolution of inelastic strain and destruction of solids is modeled numerically in terms of hierarchic systems.