A Brillouin investigation in CsHSeO4 has been performed over the temperature range 20-165 degrees C which includes two phase transitions, in particular the transition to the superionic phase near T-s = 129 degrees C. We observed strong discontinuities for elastic constants C-11, C-22 and C-33 at T-s and a broadening of the Brillouin lines above T-s. The results are discussed on the basis of a linear coupling between strains and mobile protons.