In the terms of a general approach the problem of the fast crack propa
gation in elastic bodies is considered. The time dependence of, so cal
led domain of possible fractures due to the fast crack propagation, is
obtained. The dynamic domain of possible fractures is the upper estim
ate of the zone of real fractures and thereby it takes into account su
ch important features of the fast brittle fracture as the instability
of the fast crack propagation, branching, waving, the influence of bou
ndary conditions and so on. The problem of dynamic crack initiation is
considered in some details. Within the linear fracture mechanics the
dynamic criterion of crack initiation is offered.