We investigate the shell structure of spherical nuclear bubbles in simple phenomenological shell model potentials. The shell correction energies for doubly magic bubbles may be as large as -40 MeV and probably imply a very long lifetime against spontaneous fission. Beta-stability occurs for ratios of the neutron number N to the proton number Z which differ markable from the beta-stability valley of ordinary compact nuclei. The alpha-decay probability is shown to be very small for proton rich bubbles with a moderately large outer radius. Metastable islands of nuclear bubbles are shown to exist for nucleon in the range A=450 - 3000.