Ag/Cu multilayers are deposited onto a thin Si(100) cantilevered substrate in ultra high vacuum. During deposition, the force per unit width (F/w) in the multilayers is measured continuously from the substrate curvature by a laser scanning technique. Mechanical stability and sample temperature are monitored continuously. The evolution of stress in the film during a layer deposition depends on the thicknesses of the layers beneath it. During deposition of thicker layers of either Cu or Ag, we observe increasing tensile F/w at the start of each layer. The F/w increases up to a few N/m at ∼20 nm layer thickness, and then decreases. When the thickness of each layer is less than 30 nm, the tensile stress sometimes continues to decrease even after a new interface is created. This result does not support a model for the origin of compressive stress that is based on coherent propagation of compressive strain.