  The stability of a spherically symmetric self-gravitating magnetic monopole
is examined in the thin wall approximation: modeling the interior false vacuum
as a region of de Sitter space; the exterior as an asymptotically flat region
of the Reissner-Nordstr\"om geometry; and the boundary separating the two as a
charged domain wall. There remains only to determine how the wall gets embedded
in these two geometries. In this approximation, the ratio $k$ of the false
vacuum to surface energy densities is a measure of the symmetry breaking scale
$\eta$. Solutions are characterized by this ratio, the charge on the wall $Q$,
and the value of the conserved total energy $M$. We find that for each fixed
$k$ and $Q$ up to some critical value, there exists a unique globally static
solution, with $M\simeq Q^{3/2}$; any stable radial excitation has $M$ bounded
above by $Q$, the value assumed in an extremal Reissner-Nordstr\"om geometry
and these are the only solutions with $M<Q$. As $M$ is raised above $Q$ a black
hole forms in the exterior: (i) for low $Q$ or $k$, the wall is crushed; (ii)
for higher values, it oscillates inside the black hole. If the mass is not too
high these `collapsing' solutions co-exist with an inflating bounce; (iii) for
$k$, $Q$ or $M$ outside the above regimes, there is a unique inflating
solution. In case (i) the course of the bounce lies within a single
asymptotically flat region (AFR) and it resembles closely the bounce exhibited
by a false vacuum bubble (with Q=0). In cases (ii) and (iii) the course of the
bounce spans two consecutive AFRs.
