AbstractThe stiffness characteristics of a packing of granules are influenced by the particle interactions at contacts, the void ratio, the co‐ordination number and the packing structure. A stress‐strain relationship for the packings of spheres is presented. The relationship explicitly includes the contact force‐displacement law and the parameters characterizing the packing structure. The initial moduli computed using this relationship are compared with experimental measurements and empirical equations for sands. The theoretical results are also compared with experimental results on packings of glass balls. Closed‐form solutions are derived for statistically isotropic packings under initial isotropic stress conditions. Numerical solutions for the stiffness properties are obtained for anisotropic initial stress conditions and anisotropic packing str