  Alternative verifications of Klein's theorem and the proof of $E_0=mc^2$, for
a relativistic macroscopic body are presented, using models with boundary
conditions of varying complexity, together with some refinements for the case
containing electromagnetic radiation for the simplest model. The robustness of
these models to the final result of $E_0=mc^2$, attests to the minor role
played by the Poincar\'e type stresses introduced in some of these models for
mechanical stability. Finally we caution the reader that while internal
consistency of the $E_0=mc^2$ relation for a macroscopic body in special
relativity is proved, it does not in any way furnish a proof of the relation
for a single point particle, for this would imply that one is able to prove the
postulates of special relativity from the premises of the theory itself.
