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All 13 elastic constants of a vapor grown, uncut, anthracene single crystal were determined from acoustic phonon velocities obtained by the Brillouin scattering method. The phonon velocities are plotted for three crystallographic planes containing the crystal axis. The relationships between phonon velocities and lattice dynamics are discussed. A minimizing procedure is introduced for converting phonon velocities of low symmetry systems into elasticity coefficients. This is shown to have several advantages over previous methods used. The results are compared with those obtained by previous studies of anthracene elastic constants.