The auto-balancing mechanism is used in the spin-dry regime of the laundry machine. The high rotating speed and unbalanced mass inside the drum create centrifugal force, which is the cause of vibration. The auto-balancing mechanism consists of a set of balls in the circular guiding track. During the spin-dry process, the balls settle in the opposite position to an unbalanced mass. The centrifugal force of the balls compensates the one of the unbalanced masses. The paper deals with the non-linear numerical simulation of the imbalance settlement and the following parametric study. The solution to the problem is demonstrated on an industrial laundry machine with a maximum capacity of 7 kg of dry laundry and a maximum rotating speed of 930 rpm. The proposed numerical model allows us to investigate the behavior of the auto-balancing mechanism and predict the vibration amplitudes of the system.