The phenomenon of damage, described from a physical point of view in Chapter 1, and then presented schematically in Chapter 3, represents surface discontinuities in the form of microcracks, or volume discontinuities in the form of cavities. It, therefore, involves a rheological process quite different from deformation, although the initial causes of the two phenomena are identical: movement and accumulation of dislocations in metals, modification of intermolecular bonds in organic materials, microdecohesion in minerals. Damage is marked by pronounced irreversibility; the traditional thermomechanical treatments can only partially remove the defects caused by it. Macroscopic fracture has been studied for a long time. Around 1500, Leonardo da Vinci was already preoccupied with the characterization of fracture by means of mechanical variables. A number of failure criteria, i.e., functions of components of stress or strain, characterizing the fracture of the volume element have been proposed (e.g., by Coulomb, Rankine, Tresca, von Mises, Mohr, Caquot). However, it is only quite recently that concern has been directed towards modelling the progressive deterioration of matter preceding the macroscopic fracture. The development of damage mechanics began in 1958. In that year, Kachanov published the first paper devoted to a continuous damage variable, conceived within the framework, limited indeed, of creep failure of metals under uniaxial loads. This concept was taken up again in the seventies, mainly in France (Lemaitre & Chaboche), Sweden (Hult), England (Leckie), Japan (Murakami) and extended to ductile fracture and fatigue fracture.