A dynamic tensile strength of rocks and concrete is studied in a wide range of strain rates using a structural-temporal approach. An idea of a material's fracture incubation time, taken as a scale dependent material constant and as a primary measure of the reaction of materials subjected to dynamic loading, was applied to explain the instability of the ultimate critical stress values in rock materials and concrete. Temporal dependencies (strength - strain rate; pulse amplitude pulse duration; maximum stress - pulse duration) of the spall strength for short pulse and high rate loading of dry and saturated concrete are compared and discussed. A phenomenon of the greater ultimate stress of concrete and rocks with the highest relative humidity under dynamic loading is explained. It is shown that conventional fracture criteria based only on the strain rate dependence taken from a usual linear loading law may give ambiguous results being applied for other shapes of the pulse. Application of these criteria to the case of short pulse load indicate that they are not adapted to the estimation of threshold loading parameters in the case of non-linear loading history. On the contrary, it is proved that the incubation time fracture model based on a set of material parameters, invariant to the loading history, is applicable for a broad range of load pulse types and shapes.