In this paper, we study the axisymmetric vertical instability of elongated configurations, including the effect of volumetric three-dimensional conducting structures surrounding the plasma. In order to deal with the huge computational models arising from the realistic geometrical description, a GPU-based (graphics processing units) acceleration is pursued. The method is applied to some ITER configurations, for which the open-loop growth rates, the input–output transfer functions and the gain and phase margins are computed.