In this, the first part of the survey we have discussed only certain aspects of dynamic fracture mechanics. The surveyed material has been selected with a preference for the most highly developed parts of the theory, specifically those elements which have direct bearing on the second part of the survey. We have also included information on the dynamic fracture mechanics of initially stressed materials, in the development of which one of the authors has been a major contributor. Since many problems of dynamic fracture mechanics have been overlooked in the survey, we have added supplementary references to the literature. Various aspects of the strength and fracture of materials under dynamic loading are set forth in [11, 12, 40, 57, 60, 73, 80, 83]. Criteria of the initiation, motion, branching, and arrest of cracks are discussed in [7, 9, 60, 102, 111, 113, 124]. Among the most interesting elements of dynamic fracture mechanics are the problems of crack propagation. Certain analytical results pertinent to this topic have been obtained in [43-45, 47, 67-72, 78, 87, 92, 96, 97]. © 1995 Plenum Publishing Corporation.