A numerical analysis was carried out 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, it was found that a high-Z radiation shield was necessary to screen the DT fuel from the radiation coming from the surrounding hot material. Since high-Z material opacity is only weakly density dependent, the analysis 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 these kinds of targets was studied by introducing a small spatial non-uniformity on the external surface of the lead shielding. Targets with low-density shields were also tested with a beam intensity perturbation. Since density gradients were very sharp and ablation was practically absent, these implosions were found to be Rayleigh-Taylor unstable. With the use of the full hydrodynamic-radiative model with a non-linear heavy ion energy deposition and mesh correction, it was possible, to follow the evolution in the non-linear regime.