  In the present paper we provide a description of complete Calabi-Yau metrics
on the canonical bundle of generalized complex flag manifolds. By means of Lie
theory we give an explicit description of complete Ricci-flat K\"ahler metrics
obtained through the Calabi ansatz technique. We use this approach to provide
several explicit examples of noncompact complete Calabi-Yau manifolds, these
examples include canonical bundles of non-toric flag manifolds (e.g. Grassmann
manifolds and full flag manifolds).
