Working methods include rolling, forging, extrusion, and drawing. The most basic of these is rolling. When a wide strip is rolled between two rolls, it is possible to neglect the deformation in the width direction and treat it merely as two-dimensional deformation in the thickness and length directions, except at the edges of the strip. Vertical stress P and horizontal stress Q are generated in the material between the rolls. P is a stress caused by the compressive load from the rolls, while Q is a stress generated when the deformation in the rolling direction is restrained by the portions of the strip before and after the strip in contact with the roll. Frictional force Pr is generated by the friction between the material surface and the roll surface. On the entry side, this frictional force acts in the direction of delivery, because the circumferential speed of the roll is higher than the material speed. On the delivery side, however, the frictional force acts in the direction of entry, because the material speed is higher. The point at which the two speeds become equal is called the neutral point. Taking a micro volume which has unit length in the width direction of the roll in the oblique-lined region of Fig.(a), if stress P and stress Q are assumed to be constant within the thickness, and the friction coefficient is assumed to be constant over the whole arc of contact, Eq. 1 can be derived by considering the force balance in the horizontal direction. Equation 2 is a yield criterion which shows that, in order for the material to develop plastic deformation, the shear stress generated by stresses P and Q must reach the shear yield stress of the material. P and Q can be calculated by solving Eqs. 1 and 2. The distribution of vertical stress P is shown in Fig.(b), where stress P has its peak at the neutral point. The rolling force per unit width is calculated by integrating stress P over the whole arc of contact. Furthermore, the rolling torque can be calculated by integrating the moment around the roll shaft caused by stress P. The rolling force is the most basic value used in the determination of the deformation induced by a rolling mill and the resulting strip thickness on the delivery side. It must be evaluated as accurately as possible. When dealing theoretically with improvements in the thickness accuracy and profile of a rolled strip, it is necessary to reflect, in the rolling force, both the distribution of stresses in the thickness direction and the deformation of strip in the width direction. A finite element method which permits three-dimensional analysis can be used for this purpose. Heat is generated by the deformation of the material and the friction between the material and the rolls, consequently, the temperature of the rolls and of the material rises, and roll wear also occurs. This results in the occasional sticking of the rolls to the material. Water and/or rolling oil are supplied to the contact area between the rolls and the material as a means of lubrication to reduce the friction, and hence the rolling force and rolling torque, thereby minimizing these problems. Taking the above factors into account, several methods of determining rolling force and its widthwise distribution have been developed. The optimum choice will depend upon the local conditions under consideration.