The paper briefly reviews progress in numerical simulations of dynamic crack propagation and fracture of initially intact media and presents examples of simulations utilizing finite element method with embedded dynamic fracture criterion based on the concept of incubation time of brittle fracture introduced by Petrov and Morozov. The examples include dynamic fracture initiation, propagation arrest, and evolution of fracture zones in initially intact media. It is demonstrated that this approach is capable to give an accurate description of all the variety of phenomena associated with dynamic fracture. An important feature of the approach, distinguishing it from the majority of other dynamic fracture criteria is the necessity to introduce but one additional material parameter, easily evaluated experimentally, in order to predict dynamic fracture.