We briefly review the elastic properties of granular materials, as explored in numerical studies of simple model materials by the "discrete element method " (DEM). Elastic or quasielastic responses are obtained as stable contact networks are probed with negligible friction effects. Elastic moduli, at the macroscopic scale, or contact stiffnesses at the contact network scale, have very limited influence on macroscopic constitutive laws ruling quasistatic deformation and inertial flow. The elastic moduli nevertheless provide useful indirect information on internal variables such as coordination and fabric. Singularities in the tensor of elastic moduli are related to the proximity of failure in the microscopic sense (contact network) but not in the macroscopic sense (yield condition). Elastic properties are also useful in the characterization of the directional dependence of incremental stress-strain response, a key ingredient in the identification of instabilities causing localization phenomena.