  Magnetic materials generate demagnetizing field that depends on geometry of
the sample and results in a shift of magnetic resonance frequency. This
phenomenon should occur in porous nanostructures as well, e.g., in globally
anisotropic aerogels. Here we report results of nuclear magnetic resonance
(NMR) experiments with liquid $^3$He confined in anisotropic aerogels with
different types of anisotropy (nematic and planar aerogels). Strands of
aerogels in pure $^3$He are covered by a few atomic layers of paramagnetic
solid $^3$He which magnetization follows the Curie-Weiss law. We have found
that in our samples the NMR shift in solid $^3$He is clearly seen at ultralow
temperatures and depends on value and orientation of the magnetic field. The
obtained results are well described by a model of a system of non-interacting
paramagnetic cylinders. The shift is proportional to the magnetization of solid
$^3$He and may complicate NMR experiments with superfluid $^3$He in aerogel.
