The nine adiabatic elastic stiffness constants of single-crystal forsterite (Mg₂SiO₄) have been measured as a function of hydrostatic pressure and temperature using a pulse super-position technique. The pressure dependence was linear, within experimental error, for all nine coefficients up to 10 kb. Temperature measurements were made in the range from 300° to 700°K. At lower temperatures some curvature was present, but above 500°K the data were linear. The nine adiabatic stiffnesses and their isothermal pressure derivatives at 25°C are presented, and the isobaric temperature derivatives are given at zero pressure in the high temperature limit above 500°K. The elastic constants and their pressure derivatives agree approximately with theoretical data for a hexagonal close-packed structure of oxygen anions assuming only nearest neighbor interactions and central forces. This agreement indicates that the elastic properties of forsterite are predominantly determined by the oxygen anion framework. In addition, the results were used to calculate the isothermal pressure dependence of the volume and of the lattice parameters of forsterite at high pressure from the Murnaghan and Birch equations of state.