A fibre-optic frequency shifter based on the use of flexure waves to produce a travelling perturbation which couples the polarization modes of birefringent optical fibre is described. In experiments, frequency shifts of about 790 kHz were produced. A dispersion relation for the flexure waves in the fibre has been derived and was shown to be valid in experiments. The device is described using coupled mode theory, and it is shown that optimum mode coupling will occur when the wavelength of the flexure waves is twice the birefringent beat length of the fibre.