Introduction. It has been theoretically established and experimentally confirmed that the elastic deformations of rolls and strips in cold rolling have a significant and, in the case of thin rod rolling, a crucial effect on all process parameters.Problem Statement. The influence of the elastic-plastic interaction of a thin strip with rolls, the tension, the temperature and rate of deformation, and the strength of strip material shall be taken into account for developing a modern theory of longitudinal cold rolling.Purpose. Modeling and forecasting the parameters of cold rolling of thin and extra thin strips.Materials and Methods. To solve this problem, the conditions of rolling strips made of 08kp steel with different degrees of preliminary metal hardening, which reflected the features and regularities of hardening the strip material in the multicellular state line, have been modeled. The partial relative reductions vary within 0.02—0.35,with the initial data corresponding to the most characteristic conditions of cold rolling of thin and extra thin steel strips on operating mills taken.Results. The quantitative data on the influence of the strip thickness, at the entrance to the deformation zone, partial and preliminary relative reduction during cold rolling on the process conditions with the least force. For the first time, the conditions and range of partial relative reductions for the cold rolling process of thin and extra thin strips with the least force have been determined. It has been established that in the case of cold rolling of thin and extra thin strips made of unriveted and pre-hardened steel, varying partial relative reductions within the rangefrom 0.1 to 0.30—0.35 provides the realization of process with the least force.Conclusions. The implementation of cold rolling process with the least force is advantageous in terms of energy saving and manufacturability, as it allows reducing the specific consumption of electricity and expanding the range of cold rolling mills for smaller thicknesses of rolling strips and indicates the need to determine conditionsfor such a process.