It is known that the {100} and {111} planes of cubic crystals subjected to uniaxial deviatoric stress conditions have strain responses that are free from the effect of lattice preferred orientation. By utilizing this special character, one can unambiguously and simultaneously determine the mean pressure and deviatoric stress from polycrystalline diffraction data of the cubic sample. Here we introduce a numerical tensor calculation method based on the generalized Hooke's law to simultaneously determine the hydrostatic component of the stress (mean pressure) and deviatoric stress in the sample. The feasibility of this method has been tested by examining the experimental data of the Au pressure marker enclosed in a diamond anvil cell using a pressure medium of methanol–ethanol mixture. The results demonstrated that the magnitude of the deviatoric stress is ~0.07 GPa at the mean pressure of 10.5 GPa, which is consistent with previous results of Au strength under high pressure. Our results also showed that even a small deviatoric stress (~0.07 GPa) could yield a ~0.3 GPa mean pressure error at ~10 GPa.