Dynamic loadings produce high stress waves leading to the fragmentation of brittle materials such as ceramics, concrete, glass, and rocks, or ductile materials such as steels and alloys. The main mechanism used herein to explain the change of the number of fragments with strain and stress rates is an ob-scuration (or shielding) phenomenon associated with cracking or cavitation. A probabilistic framework, which is based upon a Poisson point process, is introduced. Nonlocal (in space and time) expressions are obtained to account for multiple crack initiations or void nucleations, and their subsequent growth. This approach allows characteristic parameters (i.e. size, stress, stress rate, and time) involved in the fragmentation processes to be introduced. Examples are discussed to illustrate the use of these characteristic parameters in the analysis of dynamic fragmentation of brittle materials and spallation of tantalum.