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The dynamical stability of massive thin shells with a given equation of state (EOS) (both for the barotropic and non-barotropic case) is here compared with the results coming from thermodynamical stability. Our results show that the restrictions in the para-meter 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 relating the pressure  P , the energy density    $$\sigma $$   σof the matter on the shell, and its radius  R , namely    $$P=P(R, \sigma )$$    P  =  P  (  R  ,  σ  ).

Thermodynamical and dynamical stability of a self-gravitating uncharged thin shell