A model for the coupling of Kelvin-Helmholtz unstable fast cavity modes to field line resonances (FLRs) is presented. We consider a bounded, nonuniform magnetospheric flank separated from a semi-infinite, field-free, flowing magnetosheath by an infinitely thin magnetopause. Fast cavity modes may become unstable for sufficiently high flow speeds, and we find that for any flow speed there is a common phase speed at which all the harmonics have their maximum growth rate. The common phase speed is less dependent on the equilibrium structure within the magnetosphere than on the local structure of density ratio and relative velocity jump at the magnetopause. We perform a local analysis of the reflection and transmission of modes at the magnetopause. By requiring the spontaneous radiation of modes from the magnetopause, we may predict a phase speed at which we would expect the maximum growth rate to occur for any set of parameters. These predicted phase speeds are found to be in agreement with both those found by our model and observations of FLRs that are observed simultaneously at different latitudes. ¿ 1999 American Geophysical Union