Summary: 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 spacetime 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, a negative ${\Lambda}$ provides a never-ending process of evolution, 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 both non-periodic and inflationary expansion independent to the sign of ${\Lambda}$ term.

##### MSC:

83C55 | Macroscopic interaction of the gravitational field with matter (general relativity) |

83F05 | Relativistic cosmology |