  We study spin dynamics of a normal Fermi liquid taking into account the
demagnetizing field produced by the spin system itself. Linear solutions of the
spin dynamics equations in the form of standing spin waves in a finite volume
of liquid are found. At almost all known experimental conditions the influence
of demagnetizing field can be satisfactorily described by the first order of
perturbation theory. We carried out perturbational calculations for two
geometries of experimental cell -- spherical and finite-cylindrical. We
performed also exact numerical simulations of the spin wave spectra in a
spherical cell at an arbitrary strength of the demagnetizing field.
  The obtained results are applied in particular to conditions of recent
experiment (G.Vermeulen and A.Roni, Phys. Rev. Lett. 86, 248 (2001)) related to
the problem of zero temperature transverse relaxation in a polarized Fermi
liquid. We found that not taking into account demagnetizing field leads to
negligible errors in the measured relaxation time, thus supporting the
conclusion of the absence of zero temperature spin wave damping.
