  We study the evolution of a homogeneous, anisotropic Universe given by a
Bianchi type-I cosmological model filled with viscous fluid, in the presence of
a cosmological constant $\Lambda$. The role of viscous fluid and $\Lambda$ term
in the evolution the BI space-time is studied. Though the viscosity cannot
remove the cosmological singularity, it plays a crucial part in the formation
of a qualitatively new behavior of the solutions near singularity. It is shown
that the introduction of the $\Lambda$ term can be handy in the elimination of
the cosmological singularity. In particular, in case of a bulk viscosity, it
provides an everlasting process of evolution ($\Lambda < 0$), whereas, for some
positive values of $\Lambda$ and the bulk viscosity being inverse proportional
to the expansion, the BI Universe admits a singularity-free oscillatory mode of
expansion. In case of a constant bulk viscosity and share viscosity being
proportional to expansion, the model allows oscillatory mode accompanied by an
exponential growth even with a negative $\Lambda$. Space-time singularity in
this case occurs at $t \to -\infty$.
