The dense packing of particulate assemblies is an enduring theoretical and practical problem. In spite of its apparent simplicity, this problem still remains challenging. Recent progress in the performance of computers boosted the development and realization of a number of effective packing algorithms. Yet, because of the complexity of the problem, many of existing methods have difficulties in handling large numbers of particles. A simulation model is proposed to overcome this. The model assumes that the centers of the spheres are randomly generated at the intersections of a cubic lattice. The largest possible spheres are packed first; subsequent spheres are limited by the set of minimum diameters, which is specified by the constraints imposed by two major parameters imitating the compaction gradient: a reduction coefficient and the number of packing trials. Importantly, the packing arrangements are not defined by the initially specified particle size distribution (as considered by many existing packing algorithms), but rather the most dense particle size distribution, along with the corresponding value of packing degree, is generated by the proposed model. Based on these criteria, a very fast algorithm was developed for simulating of the dense packing of large assemblies of particulate, spherical material (in the order of millions of particles). Using this approach, the influence of geometrical parameters and model variables on the degree of packing and the corresponding distribution of particles was studied. (C) 2004 Elsevier B.V. All rights reserved.