Two gold powder samples, one with average crystallite size of ≈30 nm (n-Au) and another with ≈120 nm (c-Au), were compressed under nonhydrostatic conditions in a diamond anvil cell to different pressures up to ≈60 GPa and the x-ray diffraction patterns recorded. The difference between the axial and radial stress components (a measure of the compressive strength) was estimated from the shifts of the diffraction lines. The maximum micro-stress in the crystallites (another measure of the compressive strength) and grain size (crystallite size) were obtained from analysis of the line-width data. The strengths obtained by the two methods agreed well and increased with increasing pressure. Over the entire pressure range, the strength of n-Au was found to be significantly higher than that of c-Au. The grain sizes of both n-Au and c-Au decreased under pressure. This decrease was much larger than expected from the compressibility effect and was found to be reversible. An equation derived from the dislocation theory that predicts the dependence of strength on the grain size and the shear modulus was used to interpret the strength data. The strength derived from the published grain size versus hardness data agreed well with the present results.