Abstract: The paper discusses the dynamic propagation of cracks in brittle materials under various loads. The crack propagation is studied under both quasi-static and the shock-pulse loading conditions. Particular attention is paid to the dependences characterizing the crack propagation and having a non-stationary character. Thus, for the case of crack propagation under quasi-static loading, the crack velocity oscillations phenomenon is investigated. The problem related to the scatter of the stress intensity factor values which is observed in a number of experiments in course of the crack propagation under high-rate loading conditions is studied. The studies have been carried out using the finite element method with the structure–time fracture which is introduced into the computational scheme and which fundamentally determines the discrete mechanism of the fracture processes at a given scale level. Both quantitative and qualitative comparison of the calculation results with the available experimental data has been carried out. It is shown that taking into account the spatial and temporal discretization of the process makes it possible to explain a number of experimentally observed effects that do not fit into the traditional theoretical concepts of the dynamic fracture theory.