In the general framework of non-linear elasticity, a subtle effect of plasticity recently observed in alloys at room temperature, i.e. the gliding instability of dislocations near axi-symmetrical precipitates, has been explained by means of static atomistic simulations. It is demonstrated that the interaction usually neglected between three sources of strain identified as the dislocations, the external applied strain and the precipitates is responsible for the unusual localized cross-slip of the dislocations from the {111} to {100} planes in zone with the axis of the precipitates. The static atomistic simulations performed at 0 K have clearly shown that the modification of the inter-planar distance in the neighborhood of the precipitates leading to a local modification of the shearing properties is at the origin of this gliding in {100} planes recently observed in Al-Mg-Si alloys 6056. It is believed that the third-order interaction emphasized here plays a key role in many other problems such as creep of solids under irradiation for example.