The three-dimensional particle packing process is simulated using Lahey FORTRAN 90 as a programming language running on a personal computer. Particle clusters constructed with rearrangement which occurs during packing have higher average coordination number and packing density than particle clusters rearranged after packing. Rearranging particles can not completely block other particles from entering pore volume in 3-dimensional packing unlike in 2-dimensional packing. It is found that there is a region of instability where lower packing density results from the destruction of the ordered packing.