The mixed regime of lubrication is most frequently encountered in cold strip rolling processes. A model is presented hereafter. The lubrication at the interface is closely coupled with the mechanics of the rolling process. Therefore, the proposed model combines a macroscopic model of rolling (elastic-plastic slab method) with a microscopic mixed lubrication model, consisting of a Reynolds equation for rough surfaces (describing the formation of the lubricant film) and an equation for the evolution of roughness, describing the conformation of the strip surface to the roll. The bases of the model are presented and compared to models in the literature; its hypotheses and results are discussed, a few applications are given.