Abstract: The stress-strain relationship under simple compressionwas derived according to the theory of Hertz, using the principle ofvirtual work for an assembly of mono-size spheres with regular packing, and the results were compared with those by thediscrete element simulation with the code TRUBAL developed by Thornton.A good agreement between both results was shown. Furthersimulation for an assembly of mono-size spheres with a random packing wascarried out, and a fitting expression of stress-strain relationship forthe random packing was proposed.