The existence of two surface acoustic waves, the Rayleigh wave and the second leaky wave, on X-cut LiTaO3 has been detected using Brillouin scattering. Evidence of dispersion between ultrasonic and hypersonic velocities was found for both surface and bulk acoustic waves. Elastic constant values were determined from a simultaneous least-squares fit of the angular dispersion data for the longitudinal and the two transverse bulk acoustic modes.