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Field line resonances are thought to be excited by sources either at themagnetopause or outside it. Recent observations suggest that they may beassociated with coherent oscillations or pressure pulses in the solar wind.In either case the excitation mechanism can be understood by considering theincidence of a harmonic wave on the magnetopause from outside themagnetosphere. Calculations are performed in a plane stratified model thatconsists of (i) a magnetosheath region streaming tailward at uniform velocity(ii) a sharp boundary representing the magnetopause, (iii) a magnetosphereregion in which the Alfv\ue9n speed increases monotonically with distance fromthe magnetopause. The structure implies the existence of a propagating regionwithin the magnetopause bounded by a reflection level or turning point.Beyond this is a region in which waves are evanescent and a resonance level.The reflection and transmission of harmonic waves incident from themagnetosheath is considered in this model. It is shown that, in most cases,because of the mismatch between the magnetosphere and the magnetopause, thewave is reflected from the magnetopause with little penetration. At criticalfrequencies corresponding to the natural frequencies of the cavity formedbetween the magnetopause and turning point the signal excites the cavity andmay leak evanescently to the resonance. The calculation includes the effectof the counter-streaming magnetosheath and magnetosphere plasmas on the wave.This can lead to amplification or attenuation. The nature of the processesthat lead to transmission of the wave from magnetosheath to resonance areconsidered by synthesising the signal from plane wave spectra. A number ofmechanisms for exciting cavity modes are reviewed and the relationship of thecalculations to these mechanisms are discussed. Observations needed todiscriminate between the mechanisms are specified

Excitation of field line resonances by sources outside the magnetosphere