The dependence of ch6 in ferromagnetic Tb on a magnetic field applied along a hard axis in the basal plane has been studied experimentally. It has been predicted that c66 should vanish at the second-order transition from a phase where the magnetisation is parallel to the field to a phase which has a finite moment perpendicular to the field. Although it has not been possible to detect the ultrasonic waves in the close neighbourhood of the transition, cS6 is found to be substantially reduced at fields slightly higher than the critical value. The observed behaviour of c66 can be described quite accurately, at all temperatures below the Curie point, by a random-phase theory without the use of any free parameters,