Good surface finish is an important requirement for many stainless steel products essentially in terms of brightness. This article deals with an original numerical approach proposed in order to better control workpiece roughness during cold rolling. As a first step, to supply the numerical model, the blasted strip rheology is identified using an inverse finite element methodology based on Vickers indentations. As a second step, a fluid-structure strong coupling model is proposed to determine the flattening of steel strip asperities during the first passes of a cold rolling sequence. Fluid flowrate between each valley is solved using local Reynolds' equations. The volume of the lubricant trapped and its pressure are updated on the cold rolling model. At the same time, asperities are deformed from the entry to the exit to reach their final shape. Roughness sensitivity to the industrial process parameters, to the rheological parameters, and to the lubricant rheology is discussed.