Most available results of investigations and devel opment that deal with improving the process of cold rolling of thin strips belong to continuous multistand mills. However, some metallurgical enterprises in Rus sia have recently put into operation new reversing mills to produce cold rolled strips of a narrow grade range, such as electric steel strips (in particular, high mag netic permeability steel strips). The strips made of such steels are characterized by specific magnetic properties and high plastic deformation resistance, which is threefold that of conventional carbon steels.Metallurgists in some metallurgical enterprises, where only plate multistand mills are operative, think about putting into operation reversing mills, since the use of a reversing mill is economically efficient at an annual output of 500-550 ths t of a certain grade range specified by the market requirements. The use of a reversing mill substantially decreases the capital expenditure and operating costs related to mainte nance and depreciation of equipment.As for the economy of energy, this problem needs a special consideration, since the technological schemes, the equipment arrangement, and the operat ing conditions of reversing and continuous mills are substantially different. Therefore, the methods of energy saving developed for continuous mills can only be partly applied to reversing mills [1][2][3].The purpose of this work is to develop a technique for calculating energy effective conditions for cold rolling of thin steel strips in a reversing mill. This tech nique is based on the mathematical model of interre lated technological, energy-force, and thermal parameters of a reversing mill [4,5]. To illustrate this technique, we chose the conditions of rolling of strips made of a high magnetic permeability transformer steel. The following condition must be met to ensure the given magnetic properties: the strip temperature at the exit from the deformation zone in the two-three last passes should be 180-220°C. This condition is the main cause of joining technological, energy-force, and heat calculations into one mathematical model. The main principle of minimizing the energy in cold rolling that was earlier used in continuous mills is as follows [1-3]:(i) At a given total reduction (which is determined by the difference between the thicknesses of hot rolled semiproducts and a ready cold rolled sheet), the par tial reductions are varied and redistributed between mill stands so that the maximum possible reductions are in the first stands, where the metal has the mini mum yield strength, and the minimum reductions are in the last stands, where the yield strength is maximal because of work hardening.(ii) The forward pull of a strip is increased in each stand to the values that exclude its break in rolling. As a result, the main drive of a working stand is unloaded, and the effect is higher than the additional energy con sumption in the drive that appears in the next stand or a reel.The algorithm of optimizing the cold rolling condi tions us...