  We study magneto-elastic oscillations of highly magnetized neutron stars
(magnetars) which have been proposed as an explanation for the quasi-periodic
oscillations (QPOs) appearing in the decaying tail of the giant flares of soft
gamma-ray repeaters (SGRs). We extend previous studies by investigating various
magnetic field configurations, computing the Alfv\'en spectrum in each case and
performing magneto-elastic simulations for a selected number of models. By
identifying the observed frequencies of 28 Hz (SGR 1900+14) and 30 Hz (SGR
1806-20) with the fundamental Alfv\'en QPOs, we estimate the required surface
magnetic field strength. For the magnetic field configurations investigated
(dipole-like poloidal, mixed toroidal-poloidal with a dipole-like poloidal
component and a toroidal field confined to the region of field lines closing
inside the star, and for poloidal fields with an additional quadrupole-like
component) the estimated dipole spin-down magnetic fields are between 8x10^14 G
and 4x10^15 G, in broad agreement with spin-down estimates for the SGR sources
producing giant flares. A number of these models exhibit a rich Alfv\'en
continuum revealing new turning points which can produce QPOs. This allows one
to explain most of the observed QPO frequencies as associated with
magneto-elastic QPOs. In particular, we construct a possible configuration with
two turning points in the spectrum which can explain all observed QPOs of SGR
1900+14. Finally, we find that magnetic field configurations which are entirely
confined in the crust (if the core is assumed to be a type I superconductor)
are not favoured, due to difficulties in explaining the lowest observed QPO
frequencies (f<30 Hz).
