Various authors have shown through computational modeling and analytic
analysis that elliptical galaxies flatter than E7 will undergo dynami
cal instabilities collectively known as the firehose instability. Usin
g N-body methods, Merritt & Hernquist followed the onset and evolution
of the instability in prolate shell-orbit models. We have investigate
d the evolution of the instability and eventual quiet-system geometry
of highly flattened axially symmetric oblate models. In this paper, we
study a class of homogeneous spheroids first proposed by Polyachenko.
We show that systems flatter than E7 are unstable, that they evolve t
o states which are less flat than E7 by distinct stages, and that, in
many cases, the final isophotes are boxy ellipticals. Moreover, the fi
nal axial ratios are independent of the initial flattening.