  Recent studies of the interaction of vector mesons with nuclei make possible
and opportune the study of the interaction of the $J/\psi$ with nuclei and the
investigation of the origin of the $J/\psi$ suppression in its propagation
thorough a nuclear medium. We observe that the transition of $J/\psi N$ to $VN$
with $V$ being a light vector, $\rho, \omega,\phi$, together with the inelastic
channels, $J/\psi N \to \bar D \Lambda_c$ and $J/\psi N \to \bar D \Sigma_c$
leads to a particular shape of the inelastic cross section. Analogously, we
consider the mechanisms where the exchanged $D$ collides with a nucleon and
gives $\pi \Lambda_c$ or $\pi \Sigma_c$. The cross section has a peak around
$\sqrt s=4415$ MeV, where the $J/\psi N$ couples to a resonance predicted
recently. We study the transparency ratio for electron induced $J/\psi$
production in nuclei at about 10 GeV and find that 30 - 35% of the $J/\psi$
produced in heavy nuclei are absorbed inside the nucleus. This ratio is in line
with depletions of $J/\psi$ though matter observed in other reactions.
