This paper presents a micromechanics model for the elastic sti!ness of a non-spherical granular assembly. The microstructural continuum model of ideal spherical assembly is extended for non-ideal assembly. The presented work takes the e!ects of gradation, shape, and preferred orientation into account by introducing a directional distribution function of branch-vector length. The microstructure of a granular assembly is described by the distributions of packing structure, branch-vector length, and particle number per unit volume. These distributions account or the random nature of a realistic granular material. The microfeatures relevant to the description of non-deal particle assembly are elaborated. The in#uences of various directiondependent and direction-independent microfeatures on the elastic sti!ness are demonstrated. Hypothetical non-ideal granular assemblies are used to study the e!ects of gradation, shape and preferred orientation. Based on the proposed model, the paper discusses the inherent anisotropy in a non-ideal granular assembly. The presented work also makes use of a generalized static hypothesis to estimate the contact-force distribution for speci"c microstructure and stress state. With the estimated contact-force and the Hertz}Mindlin contact theory, the elastic sti!ness of a particulate assembly can be evaluated. Hence, the e!ects of geometric fabric and anisotropic stress state on the elastic sti!ness can be deliberated. Consequently, the e!ects of geometric fabric and kinetic fabric of a natural granular material can be evaluated independently. It is shown that the proposed model can reasonably capture the phenomena of inherent anisotropy and stress-induced anisotropy of a non-spherical granular assembly under small strain. Copyright