The authors start with the formulation of continuum damage mechanics (CDM) by Kachanov and its applications to some problems. Kachanov was the first who attempted to describe a creep rupture by an internal damage variable in the constitutive equations for the creep behavior. This idea was immediately related to results of macroscopic tests and could be simply generalized. The behavior of concrete is an example leading to the CDM theory. Here the authors present an investigation into the properties of ceramic matrix composites (CMC) consisting of a brittle matrix reinforced by continuous fibers. When loaded, these composites exhibit multiple matrix cracking. The authors attempt to give a CDM description for CMCs, based on results of materials science.