In this paper, an analytical model is established forinvestigating the dynamic fragmentation process of a brittle material thatcontains an array of fictitious cohesive cracks. The material expands atuniform strain rate, and the crack points are equally-spaced. Using theelastodynamic equations for the undamaged material and a linear cohesivefracture model for the separation of the cracks, the governing equations forthe stress and velocity in the material are deduced, which turned to be aninitial-boundary value problem (IBVP). By using Laplace transform technique,the IBVP is solved to obtain an exact expression for the cohesive stresshistory at the crack point. The material's fracture process is then studiedto determine the critical time when full fracture occurs, and the criticalexpansion of a unit crack body at this time. The influences of the crackspacing and the applied strain rate on the fracture and fragmentationprocess are investigated. Furthermore, by assuming that the critical crackbody expansion has the minimum value during a natural fragmentation process,the fragment size is estimated for different applied strain rates in thepresent study.