The Raman frequencies of diamond subjected to non-hydrostatic uniaxial stress along the [001] and [111] crystallographic axes have been calculated with density-functional-theory methods and the results fitted to a simple analytical form. The data are analyzed in the context of the recently proposed use of the shift of the high-frequency edge of the Raman band of diamond as a pressure scale in diamond-anvil cell experiments. Combining theoretical and experimental data, we are able to determine the stress state of the diamond anvil in ultra-high-pressure experiments. We find that shear stresses close to the tip of the anvil can reach values exceeding 1 Mbar.