All the parts that compose a rolling mill are subjected to elastic deformation by the rolling force. The amount of deformation of the rolls by the rolling force is the largest component of the vertical deformation of the whole rolling mill, accounting for 60-70% of the total amount of the deformation. The amount of deformation of the housing and screw-down device each account for 10-20%. As shown in the figure, rolls in a 4-high rolling mill are subjected to four kinds of deformation: (i) deflection of the back-up rolls, (ii) deflection of the work rolls, (iii) flattening of the work rolls caused by contact with the back-up rolls and material, and (iv) flattening of the back-up rolls caused by contact with the work rolls. The amounts of these four types of deformation have been analyzed theoretically. The ratio of the rolling force to the amount of vertical deformation of the whole rolling mill, including the deformation of the roll, screw-down device, and housing, is called the mill modulus. The mill modulus is 500-1,000 ton/mm for plate rolling mills and 400-600 ton/mm for cold rolling mills. The larger the diameter of the back-up rolls, the higher the mill modulus. A rolling force of the order of 1,000 tons is generated during rolling, so that mill deformation of more than 1mm occurs. Unless this deformation is taken into account, thickness accuracy cannot be ensured. Furthermore, because the mill modulus has a finite value, there exists a minimum thickness below which the rolling mill cannot reach. The flattening deformation of the work rolls during rolling requires corrections to the calculations of the rolling force derived from deformation theory. The deflection of the work rolls results in a widthwise distribution of strip thickness in the form of a convex crown, in which the thickness is greater at the center of the width and smaller at the edges. This widthwise difference in thickness is called the strip crown. In addition, a steep decrease in thickness occurs at both edges of the strip due to the combined effects of plastic deformation in the width direction, roll flattening, and roll abrasion. This phenomenon is called edge drop. Reducing the strip crown and edge drop is the greatest challenge for materializing accurate profile in strip rolling.