A two-scale numerical homogenization approach was used for granular materials. At small-scale level, granular micro-structure was simulated using the discrete element method. At macroscopic level, the finite element method was applied. An up-scaling technique took into account a discrete model at each Gauss integration point of the FEM mesh to derive numerically an overall constitutive response of the material. In this process, a tangent operator was generated with the stress increment corresponding to the given strain increment at the Gauss point. In order to detect a loss of the solution uniqueness, a determinant of the acoustic tensor associated with the tangent operator was calculated. Some elementary geotechnical tests were numerically calculated using a combined DEM-FEM technique.