  We examine the production of J/$\Psi$ mesons in high energy hadron-nucleus
collisions using models that account for both the initial state modification of
parton distributions in nuclei and the final state interaction of the produced
$c\bar c$ pairs. We show that, at the energies of current fixed target
experiments, J/$\Psi$ production through quark-antiquark annihilation gives the
largest contribution at $x_F > 0.5$, while gluon-gluon fusion dominates the
production at smaller $x_F$. The observed J/$\Psi$ suppression at large $x_F$
is directly connected to nuclear shadowing in deeply inelastic scattering. We
find that a $6\sim 8$mb $c\bar c$-nucleon cross section is needed to explain
the data on J/$\Psi$ suppression if a simple incoherent multiple scattering
formalism is used for the final state interactions.
