  We construct axisymmetric mass models for dwarf spheroidal (dSph) galaxies in
the Milky Way to obtain plausible limits on the non-spherical structure of
their dark halos. This is motivated by the fact that the observed luminous
parts of the dSphs are actually non-spherical and Cold Dark Matter (CDM) models
predict non-spherical virialized dark halos. Our models consider velocity
anisotropy of stars $\bar{v^2_R} / \bar{v^2_{\phi}}$, which can vary with the
adopted cylindrical coordinates under the assumption $\bar{v^2_z}=\bar{v^2_R}$
for simplicity, and also include an inclination of the system as a fitting
parameter to explain the observed line-of-sight velocity dispersion profile.
Applying these models to six of the bright dSphs in the Milky Way, we find that
the best-fitting cases for most of the dSphs yield oblate and flattened dark
halos, irrespective of assumed density profiles in their central parts. We also
find that the total mass of the dSphs enclosed within a spheroid with
major-axis length of 300 pc varies from $10^6M_{\odot}$ to $10^7M_{\odot}$,
contrary to the conclusion from spherical models. This suggests the importance
of considering shapes of dark halos in mass models of the dSphs. It is also
found that dark halos of the Galactic dSphs may be more flattened than N-body
predictions, thereby implying our yet incomplete understanding of baryonic
and/or non-baryonic dark matter physics in dwarf galaxy scales.
