  We extend recent discussions of singularity avoidance in quantum gravity from
isotropic to anisotropic cosmological models. The investigation is done in the
framework of quantum geometrodynamics (Wheeler-DeWitt equation). We formulate
criteria of singularity avoidance for general Bianchi class A models and give
explicit and detailed results for Bianchi I models with and without matter. We
find that the classical singularities can generally be avoided in these models.
