We present a numerical study of the stabilization process for a fully correlated two-electron model atom in an intense laser pulse. A comparison with calculations for a “real” 3D He atom is also done. We concentrate on the very high frequency regime, where the photon energy exceeds the ionization energy of both electrons, outer and inner. Our results show that when correlation effects are included the ionization probability (IP) is enhanced. Nevertheless, we still observe a decreasing IP within a certain intensity domain. The results from the fully correlated simulations are compared with those from simpler, approximate models. The full numerical treatment for the He atom is not yet possible. We therefore present results obtained with “single active electron” approximation and time-dependent density functional theory. Our numerical simulations can be useful for the future understanding of the stabilization phenomenon for more-than-one electron atoms.