The propagation of shear acoustic phonons in the solid materials of fused silica and BK7 was observed by optical beating Brillouin spectroscopy in the wavenumber range of 7×104<k<9×105 m-1. Remarkably improved detection sensitivity of the optical beating Brillouin spectroscopy system enabled the simultaneous observation of longitudinal and shear phonons in solid samples. The accurate estimation of the volume and shear elasticities in the isotropic solid material is thus possible. The measured ratio between the intensities of longitudinal and shear peaks is well explained by the equipartition law of the thermal fluctuation energy to these independent phonon modes with different elastic susceptibility.