For the adaptation of the roll-to-roll printing method to printed electronics, it is mandatory to increase the resolution of the register control. Therefore, it is desired to derive a mathematical model for the register and to develop a controller to reduce register error. The mathematical model of cross direction register was derived considering both a lateral motion of a moving web and a transverse position of a printing roll. The proposed mathematical model could be used to improve the performance of the cross direction (CD) register controller in a large area, roll-to-roll printing machine. The mathematical model was validated by numerical simulations and experimental verifications in various operating conditions using a multi-layer direct gravure printing machine. The results showed that the proposed model was effective in predicting the CD register in multi-layer printing.