Dynamic fracture of brittle materials is considered. Two approaches are illustrated by the examples of corundum ceramics and concrete. We propose a model for describing the process of dynamic fracture of porous corundum ceramics. Analyzing the fracture of concrete, we use an approach of phenomenological nature. In this method, criteria of fracture are expressed in terms of invariant relations between the critical values of the strains and the stresses which are used for describing the characteristics of the process on macro level. We present the numerical results for problems of impact interaction between a metal cylindrical striker and an obstacle containing a layer of corundum ceramics and between a metal cylindrical striker and concrete plates. The problems were considered both in two-dimensional (axially symmetric) and three-dimensional statements. We present the comparison between the results obtained on the basis of mathematical simulation and the results obtained from experiments.