This manuscript investigates some instability features in granular materials by considering an elementary grain arrangement on the intermediate scale. Although force chains have long been recognized as playing a basic role in the strength of granular specimens, the collaborative contribution of grain loops (grain arrangement) has been highlighted more recently. As a result, the stability of grain loops is expected to strongly govern the stability of the whole assembly. This paper shows that such elementary patterns can be destabilized even though the contact law between granules is elastic. This behavior stems from the nature of the kinematical model describing the geometrical interaction between neighboring grains.