  In the context of the Loop Quantum Cosmology we have analysed the holonomy
correction to the classical evolution of the simplified Bianchi I model in the
presence of vector fields. For the Universe dominated by a massive vector field
or by a combination of a scalar field and a vector field a smooth transition
between Kasner-like and Kasner-unlike solutions for a Bianchi I model has been
demonstrated. In this case a lack of initial curvature singularity and a finite
maximal energy density appear already at the level of General Relativity, which
simulates a classical Big Bounce.
