The stress in Co monolayers has been measured during epitaxial growth on Cu(0 0 1). The Co-induced stress is found to oscillate with a period of one atomic layer. Simultaneous stress and medium energy electron diffraction identify maximum stress for filled Co layers. Strain relaxation in Co islands leads to a reduced stress contribution of 2.9 GPa in the partially filled top layer as compared to 3.4 GPa for the filled layers. The corresponding variation of the elastic energy is 1 meV per Co atom. Atomic scale calculations reveal that the size-dependent mesoscopic mismatch is the driving force for stress relaxation in Co islands.