We carried out a numerical analysis on the stability of targets designed to produce fusion energy gains close to 100 when irradiated with an appropriate heavy ion beam. To reach such performances, we found that a high-Z radiation shield was necessary to screen the DT fuel from the radiation coming from the surrounding hot material. As opacity of high-Z materials is only weakly density dependent, we considered targets with lead shields both at solid density and with a density equivalent to that of the contiguous external material. The behaviour of both kinds of targets has been studied by introducing a small spatial nonuniformity on the external surface of the lead shield. Targets with low-density shields have been tested with a beam intensity perturbation, too. Because density gradients are very sharp and ablation is practically absent, we have found these implosions to be Rayleigh-Taylor unstable. The evolution has been followed in the nonlinear regime because the full hydrodynamical-radiative model with a nonlinear heavy ion energy deposition and mesh correction was used.