The formation of dispersive Alfv¿n resonance layers is investigated using a three-dimensional, two-fluid, magnetically incompressible model, including electron inertia and finite pressure. The equations are solved in ''box'' geometry with uniform magnetic field bounded by perfectly conducting ionospheres. Field line resonance (FLR) is stimulated within a density boundary layer with gradient transverse to ambient B; a parallel gradient in the Alfv¿n speed is also included. Numerical results show that the resonance amplitude is largest on the magnetic shell with eigenfrequency matching the frequency of the surface wave propagating on the density boundary layer. Efficient coupling between the resonant Alfv¿n wave and surface wave produces a relatively narrow FLR spectrum, even when the driver is broadbanded. Effective coupling to the external driver occurs only for long-wavelength azimuthal modes. It is shown that the parallel inhomogeneity limits radiation of dispersive Alfv¿n waves by the FLR. The results provide new insights into low-altitude satellite observations of auroral electromagnetic fields and the formation of discrete auroral arcs. ¿ American Geophysical Union 1995.