  We study the transformation of torsion-free coherent analytic sheaves under
proper modifications. More precisely, we study direct images of inverse image
sheaves, and torsion-free preimages of direct image sheaves. Under some
conditions, it is shown that torsion-free coherent sheaves can be realized as
the direct image of locally free sheaves under modifications. Thus, it is
possible to study coherent sheaves modulo torsion by reducing the problem to
study vector bundles on manifolds. We apply this to reduced ideal sheaves and
to the Grauert-Riemenschneider canonical sheaf of holomorphic n-forms.
