  We apply the dynamical modeling approach of Statler (1994b) to 13 elliptical
galaxies from the Davies and Birkinshaw (1988) sample of radio galaxies to
derive constraints on their intrinsic shapes and orientations. We develop an
iterative Bayesian algorithm to combine these results to estimate the parent
shape distribution from which the sample was drawn, under the assumption that
this parent distribution has no preferred orientation. In the process we obtain
improved estimates for the shapes of individual objects. The parent shape
distribution shows a tendency toward bimodality, with peaks at the oblate and
prolate limits. Under minimal assumptions about the galaxies' internal
dynamics, 35% of the objects would be strongly triaxial (0.2 < T < 0.8).
However, the parent distribution is sensitive to the assumed orbit populations
in the galaxies. Dynamical configurations in which all galaxies rotate purely
about either their long or short axes can be ruled out because they would
require the sample to have a strong orientation bias. Configurations in which
the mean motion about the short or long axis is either ``disklike''---dropping
off away from the symmetry planes---or ``spheroidlike''---remaining roughly
constant at a given radius---are equally viable. Spheroidlike rotation in the
long-axis or short-axis tube orbits significantly lowers the abundance of
prolate or oblate galaxies, respectively. If rotation in ellipticals is
generally disklike, then triaxiality is rare; if spheroidlike, triaxiality is
common.
