An analysis is made of the fluid-structure interactions necessary to support self-sustained oscillations of a single-mass mechanical model of the vocal folds subject to a nominally steady subglottal overpressure. The single-mass model of Fant and Flanagan is re-examined and an analytical representation of vortex shedding during 'voiced speech' is proposed that promotes cooperative, periodic excitation of the folds by the glottal flow. Positive feedback that sustains glottal oscillations is shown to occur during glottal contraction, when the flow separates from the 'trailing edge' of the glottis producing a low pressure 'suction' force that tends to pull the folds together. Details are worked out for flow that can be regarded as locally two-dimensional in the glottal region. Predictions of free-streamline theory are used to model the effects of quasi-static variations in the separation point on the glottal wall. Numerical predictions are presented to illustrate the waveform of the sound radiated towards the mouth from the glottis. The theory is easily modified to include feedback on the glottal flow of standing acoustic waves, both in the vocal tract beyond the glottis and in the subglottal region.