  The proposed hadronic and string cascade model, JPCIAE, for ultrarelativistic
nucleus - nucleus collisions based on the LUND model and the PYTHIA event
generator especially, is used to investigate the $J/\psi$ suppression due to
the nuclear absorption of a $J/\psi$ in minimum bias pA and BA collisions at
200 A GeV energy. With the different sets of reasonable formation time for
hadron and $J/\psi$ the results of $J/\psi$ suppression factor from both the
usual scenario and the Glauber - like simulations are comparable with all the
NA38 pA and BA data, except the NA50 data of Pb + Pb collisions. However, the
difference between the usual scenario and the Glauber - like simulation, hence
the difference between the dynamical simulation and Glauber theory, can not be
ignored. The sensitive effect of the hadron formation time on the $J/\psi$
suppression is studied in detail. The results seem to denote that for the
$J/\psi$ suppression the meson absorption plays role in pA as well as in BA
collisions.
