An analytical investigation of a fundamental dynamic fracture effect observed in samples with a crack under shock-wave pulse load is provided. Particular attention is paid to the phenomenon of delayed fracture. The effect can be described in the following way: the fracture in the crack tip vicinity can possibly take place after the local stresses reached their maximum value. A number of important features of dynamic fracture under the threshold and beyond threshold loads, observed in various experiments, are discussed. It was found that the experimentally registered fracture delay can be clearly explained within the framework of the structural-temporal approach based on the concept of the incubation time of fracture. The conditions for the delay are found and the corresponding analytical formulas are given. Additionally, a simple analogy based on a mass-spring model is discussed. Analytical formulas available for the oscillator model help to find some non-obvious similarities between the crack behaviour under short pulse loads and the oscillator failure due to analogous loads. It is concluded that it is essential to study threshold cases in which the most important time effects appear that do not fit into the classical concepts of strength and crack resistance – the concepts that rely on local ultimate stress and/or critical intensity factor parameters.