  The dynamical stability of massive thin shells with a given equation of state
(EOS) is here compared (both for the barotropic and non-barotropic case) with
the results coming from thermodynamical stability. Our results show that the
restrictions in the parameter space of equilibrium configurations of the shell
following from thermodynamical stability are much more stringent that those
obtained from dynamical stability. As a byproduct, we furnish evidence that the
link between the maximum mass along a sequence of equilibrium configurations
and the onset of dynamical stability is valid for EOS of the type $P=P(\sigma,
R)$.
