Results of studies of the explosive expansion of a set of shrapnel discs of natural crushing are described in the article. Set consisted of two disks of different thickness, but of a fixed total mass. The studies were carried out by computer simulation of shock-wave processes in a continuous formulation using the ANSYS/LS-DYNA program. The program of computer design foresees development of three-dimensional certainly-element model including, in accordance with symmetry of the examined system fourth part of the examined explosive system of casting block, with imposed on its knots of the proper scopes terms concerted with taken mixed Lagrangian-Eulerian approach within the framework of the continuum model. The effect of the order of installing disks of different thickness on the distribution of their mass and its velocity in the middle of the meridional angle of expansion is established. The analysis of the computer simulation presented on the basis of numerical studies on the distribution of the mass of the disks and its velocity of motion suggests that to create a narrow high-speed uniformly filled fragmentary mass of the axial flow, it is necessary to change the geometric shape of the disc so that in the central angular zones of the disks. This allows the velocity of the fragment mass to be aligned along the radius of the discs and to fill the first angular zones with the required mass of fragments.