We applied coherent Brillouin spectroscopy to solid parahydrogen, and measu
red the Brillouin spectra of longitudinal acoustic modes at 5.6 K. It was f
ound that the linewidth of these spectra is similar to 1.5 MHz. From the ob
served Brillouin shift and the crystal orientation, the elastic stiffness w
as determined as C-11 =0.355 +/-0.016 GPa and C-33 =0.432 +/-0.022 GPa.