A computer simulation for evolution of random structures of spherical particles in two dimensions (2D) has been performed by the distinct element method (DEM). The forces among the particles considered were gravity, contact force, friction force, and van der Waals interaction (VDWI). The motions of the particles considered were translation and rotation. Two-hundred-forty mono-sized spherical particles were located without overlapping inside a rigid square box by generating the coordinates of centers of the particles with the help of a random number generator. Initial packing density was only 0.4712. The particles were allowed to settle under gravity. When the coefficient of friction among the particles and between the particle and the wall of the box was 0.364, the packing density was 0.8236, which is comparable to the density of dense random packing. If there was no friction, the density was 0.8696. For small particles, VDWI was considered in the simulation. It has been found that VDWI can reduce the packing density through formation of local clusters. To study rearrangement of particles, some trajectories of a few selected particles were traced. The average coordination number of dense random packing of this simulation is similar to German's results [R.M. German, Particle Packing Characteristics, Princeton, NJ, 1989]. With the comparison, it is concluded that the DEM and the present program are valid methods for research in the behavior of random packing spheres.