The spectrum of toroidal standing shear Alfv¿n waves (SAWs) is derived for a stretched magnetic field line geometry that is approximated by the Tsyganenko 96 magnetic field model. The model is applied to field lines near the midnight meridional plane. It is demonstrated that the fundamental mode frequency for typical ambient parameters of Earth's magnetosphere is in the 1--4 mHz range. This frequency is in agreement with the measured frequency of magnetospheric field line resonances, and is up to an order of magnitude smaller than for a dipolar magnetic field. We conclude that stretching of Earth's magnetic field offers a possible explanation for anomalously low frequency SAWs observed within diffuse auroral emission (H&bgr;) produced by energetic proton precipitation in the inner plasma sheet. ¿ 2000 American Geophysical Union