The progress of failure in metals, under various loading conditions, is as- sumed to involve the degradation of a structure due to nucleation and growth of defects, such as microvoids and microcracks, and their coalescence into macrocracks. This process, generically termed damage, was first used to pre- dict material failure and rupture in-service in an elevated condition. Although damage mechanics provides a measure of material degradation on a microme- chanics scale, the damage variables are introduced to reflect average material degradation on a macromechanics scale and thus continuum damage mechan- ics (CDM) was developed. In the micro-cracking of materials under different stress conditions, damage is regarded as the progressive degradation. This ma- terial degradation is reflected in the non-linear behaviour of the structures. Non-linear analysis based on CDM provides conservative and realistic results. Since the pioneering work of Kachanov in 1958, continuum damage mechan- ics has been widely accepted to describe progressive failure due to material degradation. The reason for its popularity is as much the intrinsic simplic- ity and versatility of the approach, as well as its consistency based on the theory of the thermodynamics of irreversible processes. When the crack pro- files are not known a priori, the continuum damage mechanics approaches are computationally very attractive. CDM is a very applicable and rapidly de- veloping discipline. Now many papers are published and several international conferences, e.g., IUTAM-Symposia or EUROMECH-Colloquia, take place. Furthermore, a special International Journal of Damage Mechanics stresses the importance of this branch of solid mechanics.