A method is presented for modeling the geometrical packing of polydisperse mixtures of both spherical and nonspherical particles, which are models for filler particles used in the manufacture of polymer composites. The technique is based on the calculation of the dissipative dynamics of an ensemble of fused soft spheres at constant temperature and pressure. After validation of the method at low pressures by comparison with analytical equations of state for monodisperse and binary mixtures of hard spheres, the random packing of fused soft sphere cubes was studied. The effect of packing cubes together with spheres of varying size was then examined, with the aim of developing an understanding of how to minimize the amount of void space in composites containing angular particles. In one case, entropically driven demixing was observed in a cube-sphere mixture.