  Quantum stabilization of superheavy elements is quantified in terms of the
shell-correction energy. We compute the shell correction using self-consistent
nuclear models: the non-relativistic Skyrme-Hartree-Fock approach and the
relativistic mean-field model, for a number of parametrizations. All the forces
applied predict a broad valley of shell stabilization around Z=120 and
N=172-184. We also predict two broad regions of shell stabilization in
hyperheavy elements with N approx 258 and N approx 308. Due to the large
single-particle level density, shell corrections in the superheavy elements
differ markedly from those in lighter nuclei. With increasing proton and
neutron numbers, the regions of nuclei stabilized by shell effects become
poorly localized in particle number, and the familiar pattern of shells
separated by magic gaps is basically gone.
