  The Knight shift data on Li and Zn substituted YBa$_2$Cu$_3$O$_{6+x}$ are
analysed using an itinerant model with short-range antiferromagnetic
correlations. The model parameters, which are determined by fitting the
experimental data on the transverse nuclear relaxation rate $T_2^{-1}$ of pure
YBa$_2$Cu$_3$O$_{6+x}$, are used to calculate the Knight shifts for various
nuclei around a nonmagnetic impurity located in the CuO$_2$ planes. The
calculations are carried out for Li and Zn impurities substituted into
optimally doped and underdoped YBa$_2$Cu$_3$O$_{6+x}$. The results are compared
with the $^7$Li and $^{89}$Y Knight shift measurements on these materials.
