We report on the first direct measurement of the change of the surface stress in the reconstruction of the Au(111) and the Au(100) surfaces. For both surfaces the reconstruction relaxes the intrinsic tensile stress, by 22 percent and 5 percent, respectively. A discussion of the data on the Au(111) surface in the Frenkel-Kontorova model shows that the energy gain due to the surface stress is not quite large enough to make the reconstructed phase energetically favored without the formation of the secondary herringbone structure of the solitons. On the Au(100) surface, the gain in elastic strain energy is clearly insufficient to cause the surface to reconstruct.