  Bianchi type I cosmological models are studied that contain a stiff fluid
with a shear viscosity that is a power function of the energy density, such as
$\zeta = \alpha \epsilon^n$. These models are analyzed by describing the
cosmological evolutions as the trajectories in the phase plane of Hubble
functions. The simple and exact equations that determine these flows are
obtained when $n$ is an integer. In particular, it is proved that there is no
Einstein initial singularity in the models of $0\leq n < 1$. Cosmologies are
found to begin with zero energy density and in the course of evolution the
gravitational field will create matter. At the final stage, cosmologies are
driven to the isotropic Fnedmann universe. It is also pointed out that although
the anisotropy will always be smoothed out asymptotically, there are solutions
that simultaneously possess non-positive and non-negative Hubble functions for
all time. This means that the cosmological dimensional reduction can work even
if the matter fluid having shear viscosity. These characteristics can also be
found in any-dimensional models.
