Acoustic velocities, refractive index, and elastic constants of liquid and solid nitrous oxide (N2O) have been determined at pressures up to 4.5 GPa by applying Brillouin spectroscopy whereby the crystal orientation in a high-pressure diamond-anvil cell could be found in the same fitting analysis. In comparing these results with those of carbon dioxide (CO2), the elastic properties of an isoelectronic pair, N2O and CO2, are investigated in their pressure-induced liquid and solid I phases at room temperature.