The surface stress, in addition to the surface energy and elastic modulus, is a fundamental measure of the surface effects in a nanostructure. Here, we investigate the strong correlation between the surface stress and mechanical strain in three noble-metal (001) surfaces. For this investigation, we have developed a simple and efficient method to calculate the surface stress directly from the strained configurations in molecular statics simulations. While the surface stress of the copper (001) surface along the strained direction is almost constant, that of the gold (001) surface decreases drastically as the strain increases. We explain these different responses of the surface stress to strain in terms of the different surface relaxation occurring in different noble-metal nanoplates.