Magnetic pulsations are a robust feature of the Earth's magnetosphere. It has been suggested recently that the magnetosphere is sometimes better modeled as a waveguide rather than a cavity. This paper presents numerical simulations of linear magnetohydrodynamic (MHD) waves in an inhomogeneous, low-&bgr; waveguide. Several features predicted by recent theoretical studies are confirmed in our simulations, notably that Alfv¿n resonances are driven at frequencies corresponding to the natural frequency of the fast waveguide modes with Vg≈0 (ky≈0). ¿ American Geophysical Union 1994