Elastic stresses arising at the clean Ge𝑥Si1−𝑥/Si(001) surface, as well as at the initial stages of its oxidation, are considered qualitatively by analyzing the changes of unit cell dimensions occurring owing to the ad-dimer formation or the atomic or molecular adsorption on the unit cell surfaces. The stress character is found to be almost identical for the clean Ge𝑥Si1−𝑥/Si(001) surface and the Ge𝑥Si1−𝑥/Si(001) surface with adsorbed oxygen molecules or one to three adsorbed oxygen atoms. In addition, the surface stresses revealed a significant anisotropy: they turned out compressive along the dimer rows and three times as large as tensile stresses in the perpendicular direction (along the interdimer bonds).