A simulation algorithm was developed for modeling the dense packing of large assemblies of particulate materials (in the order of millions). These assemblies represent the real aggregate systems of portland cement concrete. Two variations of the algorithm are proposed: sequential packing model and particle suspension model. A developed multicell packing procedure as well as fine adjustment of the algorithm's parameters were useful to optimize the computational resources (i.e., to realize the trade-off between the memory and packing time). Some options to speed up the algorithm and to pack very large volumes of spherical entities (up to 10 million) are discussed. The described procedure resulted in a quick method for packing of large assemblies of particulate materials. The influence of model variables on the degree of packing and the corresponding distribution of particles was analyzed. Based on the simulation results, different particle size distributions of particulate materials are correlated to their packing degree. The developed algorithm generates and visualizes dense packings corresponding to concrete aggregates. These packings show a good agreement with the standard requirements and available research data. The results of the research can be applied to the optimal proportioning of concrete mixtures.