Observations of axial acoustic waves in multimode polymethylmethacrylate(PMMA) optical fibres are reported. Rapid electrostriction was induced in a 1.25 m length of PMMA optical fibre using a pulsed transverse electric field of ~106 V m-1. By observing the effects of birefringence on a polarised laser beam, acoustic waves travelling with a speed of1050 m s-1 were observed to travel between the fibre ends. Simple calculations indicate that these acoustic waves comprised shear waves, although propagation of surface waves could not be ruled out. The implications of these observations in terms of a new class of optical fibre sensors based on the propagation of axial acoustic waves are also discussed.