  A tensor virial approach is used to construct detailed models of 22 flattened
ellipticals. The models are combined with the new observational data: extended
surface brightness distributions, the profiles of isophotes flattening and
their twisting, the rotation curves and the velocity dispersion profiles. A key
feature of these models is a rigorous consideration of the influence of the
spatial shape of galaxies (oblate spheroid or triaxial ellipsoid) on the
dynamics, as well as the structure of the internal density layers in these
systems. For each galaxy the ratio of the rotational energy to the potential
energy was found. Comparing this ratio with the observed it is concluded that
the majority of these systems cannot have isotropic velocity dispersion
tensors. The anisotropy parameter limited to the interval 0.0-0.224. A
correlation was found between and flattening of the outer regions for giant
E-galaxies. Our results are compared with the results of other researchers. It
was found that for small fast rotators our values \b{eta} are in good agreement
with those, obtained in the ATLAS project. However, for giant E-galaxies, our
models provide better agreement with observations, than axisymmetric JAM
models. In addition, our velocity dispersion anisotropy results are in
satisfactory agreement with the results of high resolution cosmological
simulations in the Illustris project

Astrophysics of Galaxies