A stress exists in solids surfaces, similarly to liquids, also if the underlying bulk material is stress-free. This paper investigates the surface stress effect on the measured value of the Si lattice parameter used to determine the Avogadro constant by counting Si atoms. An elastic-film model has been used to provide a surface load in a finite element analysis of the lattice strain of the x-ray interferometer crystal used to measure the lattice parameter. Eventually, an experiment is proposed to work a lattice parameter measurement out so that there is a visible effect of the surface stress.