Abstract The problem of definition of power parameters for the process that takes place in superficial layers of band during drawing it through revolving rollers is considered. The analysis of superficial deformation process of tapes that are drawn between fast revolving rollers with the given speed of relative moving of surfaces of tapes and rollers has shown that in this case on a treated surface small crystal layers with high service properties are formed. The expressions for engineering account of drawing are introduced. That allows finding the rationally regime of tapes processing to achieve required quality of superficial layers. The analysis of the received equations showed that the effort of drawing increases with the increase of a degree of deformation and decreases with the increase of an initial thickness of a tape. The increase of rollers’ size leads to the growth of the effort of drawing.