We evaluate the dipolar energy in a periodic multilayer film consisting of alternating ferromagnetic and nonmagnetic layers, for magnetization perpendicular to the plane of the film, arranged in alternately polarized strip domains. The lowest‐energy state for this configuration is calculated for the case of freely mobile domain walls. Within certain limits, the layered film behaves as a uniform medium with an anisotropy arising from the layering. The relevance of the theory to experiments on Pd/Co layered films is discussed.