This work is concerned with the mathematical modeling of a cold precision leveler for heavy plates and the development of optimal control strategies for the leveling process. First, a mathematical model of the loaded leveler is developed. To model the leveler under load, a tailored finite element model of the considered machine is combined with an elasto-plastic plate model, which captures the relevant effects of the leveling process. The models are verified by measurements on an industrial leveler. Next, a novel model-based calibration method to estimate adjustment errors of the work rolls is developed and verified with measurements on an industrial leveler. Finally, optimal control strategies to compensate for the deflection of the leveler for all load phases of the leveling process are developed.