We report the complete set of elastic constants and the bulk modulus for single crystal Pb(Mg1/3Nb2/3)O3 (PMN) at room temperature obtained from Brillouin spectroscopy and molecular dynamics (MD) simulations. The bulk modulus from Brillouin is found to be 103 GPa, in a good agreement with earlier x-ray studies. We also derived the refractive index along all principal axes and found PMN to be optically isotropic, with a refractive index of 2.52 +/- 0.02. PMN shows mechanical anisotropy with A=1.7. The MD simulations of PMN using the random site model overestimate the elastic constants by 20-50 GPa and the bulk modulus is 148 GPa, but the mechanical anisotropy matches the Brillouin results of A = 1.7. We also determined the elastic constants for various models of PMN and we find variation in the elastic constants based on chemical ordering.