Three elastic constants in the orientationally disordered solid phase of methane have been determined at room temperature, as a function of pressure up to 5 GPa, by Brillouin spectroscopy developed for single crystal grown in a diamond anvil cell. It is found that the velocity of the slow transverse acoustic mode in the 〈110〉 direction is insensitive to pressure as compared with other velocities, which leads to the anomalous increasing of the ratio of the longitudinal acoustic velocity to the slow transverse one in the 〈110〉 direction. This result suggests that the rotation-translation coupling has strong pressure dependence.