The single-crystal elastic moduli of natural samples of grossular (99.0 mol % Ca3Al2Si3O12) and spessartite (94.8 mol % Mn3Al2Si3O12) have been measured by Brillouin spectroscopy under ambient conditions. From these results the adiabatic bulk moduli Ks and shear moduli μ are calculated to be Ks=168.4¿0.7, μ=108.9¿0.4 for grossular, and Ks=178.8¿0.8, μ=96.3¿0.5 for spessartite (all in units of gigapascals). A calibration of our spectrometer by determination of the elastic properties of MgO indicates that these modulus values are accurate to within twice the stated rms error. Of the major rock-forming silicate garnets, spessartite has the largest bulk modulus, and grossular has the largest shear modulus, with the possible exception of majorite (a high-pressure form of pyroxene.) Approximate values for the bulk and shear moduli of common aluminosilicate garnet solid solutions can be obtained with an estimated uncertainty of less than 3% from a linear molar average of the end-member properties. The elastic properties of pure almandite garnet (Fe3Al2Si3O12), which have thus far not been measured, are estimated as Ks=177¿3 and μ=97¿1 GPa by a linear regression analysis of extant measurements on garnet solid solutions and end-members. These same data imply, however, that a linear modulus-composition relationship may not be appropriate for all silicate garnet compositions. ¿ American Geophysical Union 1989