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 Alfvén 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 Alfvén 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 8 x 10 14 and 4 x 10 15 G, in broad agreement with spin-down estimates for the SGR sources producing giant flares. A number of these models exhibit a rich Alfvén 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).