  We report new results for the elastic constants studied in Faraday and
Cotton-Mouton geometry in Tb$_3$Ga$_5$O$_{12}$ (TGG), a frustrated magnetic
substance with strong spin-phonon interaction and remarkable
crystal-electric-field (CEF) effects. We analyze the data in the framework of
CEF theory taking into account the individual surroundings of the six
inequivalent Tb$^{3+}$-ion positions. This theory describes both, elastic
constants in the magnetic field and as a function of temperature. Moreover we
present sound-attenuation data for the acoustic Cotton-Mouton effect in TGG.
