A simulation model is proposed for the dense packing of particulate, spherical material. The model assumes that the centers of the spheres are randomly generated at the grid of the cubic lattice. The biggest possible spheres are packed first; they are limited by the sequence of minimum diameters, which are determined by a reduction coefficient and the number of packing trials. Based on these assumptions, a very fast packing algorithm was developed. Using this algorithm, the influence of geometrical parameters and model variables on the degree of packing and the corresponding distribution of particles was analyzed. According to the simulation results, three different modules are suggested to estimate the packing degree for a given particle distribution, and also to distinguish between 'initially loose' and 'initially pre-packed' conditions.