The critical attenuation (as) of longitudinal ultrasonic propagation in the vicinity of the f erroelastic-f erroelectrie transformation of GMO has been measured at frequencies (f) 31, 50, 72 and 93 MHz. The proportional relation between as and f2 is established satisfactorily in so far as the shear type phase transition is concerned. In addition, the critical exponents for the attenuation is determined: ρ=1.52 for T-Tc>0.05 K and the crossover behavior is observed.Eesults are also reported on a internal friction investigation (at f=1 Hz, 150kHz) of the ferroelastic transition of GMO, which is suggested to be caused by the moving interphase boundary. The critical stress to move the boundary is determined and it is then confirmed that the mechanism of the ultrasonic attenuation of longitudinal wave in the 2-4°direction is just contributed by the fluctuation damping.