The formation of the (2x1) oxygen stripe phase on Cu(110) at room temperature is imaged in situ with an STM and simultaneously a quantitative determination of the oxygen-induced surface stress is accomplished. The bending bar technique is utilized with the bending measured by the STM. We find that the difference Delta tau of the surface stresses of the (2x1) phase on Cu(110) and the clean Cu(110) surface is compressive for both directions, which is in accordance with the adsorption of oxygen on other surfaces. The stress depends significantly on the coverage. Quantitative aspects of these results raise an interesting issue concerning the applicability of the Marchenko-Alerhand continuum model for the self-assembly of the stripe phase.