The results of experimental and theoretical studies on the dynamic response of brittle and ductile materials are presented. The work shows the possibility of predicting the critical stress of brittle materials or yield strength of ductile materials over a wide range of strain rates on the basis of a combination of a simple theoretical approach to dynamic strength and a set of experimental data obtained using a conventional technique. The studies were carried out using fine-grained concrete and ceramic brick as representatives of brittle materials, and copper and titanium as representatives of ductile materials. The traditional Kolsky method was used to determine the strength and ductility characteristics under dynamic loading conditions of the experimental samples. The sensitivity of the critical stress characteristics of failure and yielding of the studied materials to the strain rate is shown. The incubation time approach is used to interpret the effects of strain rate. The applicability of the incubation time criterion to prediction of the dynamic behaviour of both brittle and ductile materials is shown. The presented unified experimental-theoretical approach can be applied in engineering practice to model the dynamic response of structural materials.