The natural packing structure of sand grains under gravity within cylindrical and cuboidal container has been simulated using Monte Carlo method. First

a loose packing structure is generated using reference lattice method. Secondly

Monte Carlo algorithm was launched

i.e. random displacements are imposed on sand grains; as a result

a new configuration was obtained. If overlapping exists between grains and between grains and boundaries

the new configuration is deserted. The potential energy change of particles and Metropolis law employed to identify whether the new configuration is accepted or not. The final dense packing configuration is reached by repeating the above-mentioned process. The contact detection algorithm advised by Schinner was used to identify contacts between particles

and the contact detection algorithm between particles and boundaries was also introduced in detail. The simulation results indicate Monte Carlo method is very valid for simulating sand particles packing under gravity. The simulating results can provide initial configuration for simulating flow and compaction of sand materials.