  The formulae for shadowing corrections in deep inelastic leptoproduction of
vector mesons are presented. These formulae are also applicable for
photoproduction of vector mesons constituted of heavy quarks. Our results are
conveniently presented by the definition of a damping factor giving the
reduction of the calculated cross sections due to shadowing. Our calculated
cross sections are compared with those obtained with no shadowing and with the
available experimental data including the recent data from HERA. We have also
investigated the importance of shadowing on the relationship between $\frac{\pa
F_2(Q^2,x)}{ \pa ln Q^2}$ and the cross section for virtual photoproduction of
vector mesons. A discussion of shadowing corrections to the proton's gluon
density is presented and numerical estimates are given.
