A series of computer experiments were performed to model the random packing, of spherical particles. Known algorithms for dense packing were modified to optimize density characteristics. The distribution of local density in random packs of spherical particles was investigated. The effect of boundary conditions on the density characteristics was determined, and the dimensions of the boundary distorted zone evaluated. Methods for controlling the integral density and local density distribution in packs of spherical particles were determined. These are based on the concept of density characteristics as functions of the ratio of particle sizes and numbers in a fraction, and in a mixture.