Divergent compression and rarefaction waves propagating in a target upon impact of a group low-deformable particles were numerically investigated to reveal the physical mechanisms of the increase in penetration depth. An original approach was used where a depression (crater) in a target simulated the result of impact of a previous particle. Repeated reflection of rarefaction waves from the depression wall, their arrival at the impact axis, and subsequent propagation deep in the target has been revealed. It has been supposed that these repeated rarefaction waves produces stage-by-stage local damage to the target material ahead of the particle followed by the formation of a cylindrical crack, and this eventually provides the increase in penetration depth observed in experiment.Keywords: Multiple impact, failure, finite element method.Investigations of the dynamic interaction of deformable solid bodies are limited to studying the impact of a single body with various types of target [1,2]. By now, little attention was given to the problems of impact of a group of bodies with a target and to studying the features of their collective action both experimentally and theoretically [3,4]. This situation is mainly related to the complexity of studying the process of impact of a group of bodies with targets. In experiment, it is difficult to realize a controlled projection of a group of bodies with desired distributions of the body velocities in direction and size and of the distances between the bodies over the front and in group depth; it is also difficult to measure the parameters of the bodies on approaching the target and during the interaction with the target [4-6]. An adequate numerical simulation calls for three-dimensional calculations that necessitate the use of complex numerical techniques and simultaneous computations [3]. At the same time, the collective action of a group of particles of varied size and shape on a target is realized in practice in the majority of high-speed impact events. This can be the secondary impact of a group (flow) of the target fragments that have formed behind the target after the primary impact. A primary impact can also be collective.The investigations performed have shown that the physical and mechanical features of the collective action of a group of particles essentially differ from that those inherent in single-particle impact. Lin and co-workers [5] investigated experimentally the penetration of a group of spherical steel (ShKh-15) particles of diameter d = 5 mm into a duralumin (D16-T) target of thickness h = 15 and 100 mm at an impact velocity of 1400 ± 100 km/s. This velocity can be considered moderate when the effect of the physical mechanisms of compression and heating of the medium in a shock wave is low and the leading role is played by the deformation (strength) processes of shear hardening and softening that occur on cumulative damage and heating in the region of intense plastic strain. Under the given conditions, the particles were deformed only slightly and, as a whole...