Discrete features of the dynamics of fracture of solids are analyzed. The problem of modeling of some of the specific effects of brittle fracture in the high loading rate conditions is discussed. An approach based on the system of fixed material constants describing macro-strength properties of the material is considered. New principles of material testing are analyzed. The corresponding incubation time criterion allows one to manage without the a priori given rate dependences of dynamic strength and fracture toughness. An application of the incubation time criterion to the problem of erosion is considered.