Abstract: This paper is one of the consequences of the theory of friction lines, which has been independently developed both in Europe[13] and here[1],[8],[9],[10],[11],[12].Karman’s rolling equation is modified to yield its mean-value form which is more proper for simplifying a surface problem to an one-dimensional one. Smoothly continuous solutions are obtained for the case of dry friction. This method of solution appears to have avoided the high peak feature of pressure distraction, common to all other existing solutions in this case, and is able to give account to the distinction between cold and hot rolling with .same coefficient of friction.