  Using the simulation of Katz & White we have tested the viability of X-ray
analysis for constraining the intrinsic shapes of clusters of galaxies
considering the effects of both substructure and steep temperature gradients.
We restrict analysis to aggregate cluster shapes on scales of $r\sim 1-2$ Mpc
to reduce our sensitivity to core subclustering. For low redshifts $(z\lesssim
0.25)$ the X-ray method accurately measures the true ellipticity of the
three-dimensional cluster dark matter; assuming the gas is isothermal adds only
small errors. At higher redshifts the X-ray method yields unreliable results
since the gas does not trace the cluster gravitational potential. We proffer
necessary conditions for the reliability of X-ray methods characterized by the
amount of substructure in the X-ray surface brightness images and the isophotal
shapes. We conclude that measurements of aggregate cluster shapes on scales
$r\sim 1-2$ Mpc are insensitive to core substructure on scales of a few hundred
kpc. Therefore our results suggest that the X-ray measurements of aggregate
cluster shapes by Fabricant, Rybicki, & Gorenstein and Buote & Canizares are
valid provided that they do not suffer from serious projection effects. A
substantial number of Abell clusters observed with the ROSAT PSPC will be
amenable to X-ray shape analysis.
