Crack nucleation and crack growth in polymers and other materials with hereditary behavior were studied by a number of authors [69, 155]. It is essential that cracks grow both under long-acting (constant or slowly varying) loads and under cyclic loading. In the first case one often speaks of static fatigue, in the second of cyclic fatigue. The latter includes classical high-cycle fatigue as well as low-cycle fatigue. Related phenomena occur in metals and metallic alloys at elevated temperatures loaded statically, cyclically, or both [89, 65, 119]. Structural failures due to crack growth in disks, blades and other components of power machinery are of essentially practical importance.