The adiabatic elastic moduli of a high-pressure sodium-rich majorite garnet have been measured at ambient conditions using Brillouin spectroscopy. This garnet has the composition, Na1.87Mg1.18Si4.94O12, with sodium and magnesium in eight-fold coordination and silicon in octahedral and tetrahedral coordination. While the adiabatic bulk modulus, Ks=173.5 GPa, falls within the range of common garnets, the shear modulus, &mgr;=114.7 GPa, is unusually large; sodium garnet is elastically similar to the low-pressure garnet grossular. The variation of elastic properties for garnets of differing composition within the cubic garnet structure can be expressed as a linear function of the ratio of average cation radii in the eight-fold versus the six-fold site. The cations in the AO8 polyhedra apparently brace the structure by controlling rotational freedom within corner-linked chains of alternating tetrahedra and octahedra. ¿ American Geophysical Union 1992