The single-crystal elastic moduli of the spinel (gamma) phase of Mg2SiO4 have been experimentally determined from Brillouin spectroscopy at ambient conditions. They are C11=327, C44=126, and C12=112 (GPa) yielding a bullk modulus of 184. and a shear modulus of 119 GPa. This value of bulk modulus is lower than expected from previous measurements. The elastic properties of the spinel and modified spinel (beta) phases of Mg2SiO4 are quite similar with the greatest differences related to the c axis of the beta which is relatively soft under compression. The polycrystalline acoustic velocities differ by only 1% for these two phases. Thus there sshould be no seismic discontinuity associated with th beta to gama phase transition in the mantle. The similarity of elastic properties of these two phases suggests that effects of pressure, temperature, and iron content on the elastic properties should be similar for both phases. Estimates of the effect of iron content are made from the extent data on fayalite spinnel in conjunction with the data presented here. The derivatives of elastic moduli with respect to iron content are very similar to those observed for the olivine phases. Based on comparisons with aluminate analogue compositions in the spinel structure, there is no justification to predict the pressure or temperature derivatives of the elastic moduli of these high pressure phases at this time.