An analysis of fragmentation due to dynamic stress loading is presented which provides analytic functions for the distributions in fragment sizes. The analysis is restricted to one-dimensional bodies under uniform tensile loading. Concepts of survival statistics are used to account for spatially random fracture nucleation. Fragment size distribution curves for both brittle and ductile fracture are derived, and the curve for the latter is compared with experimental data. Fragment distribution curves are shown to depend on both material deformation properties and loading conditions.