For the adaption of roll-to-roll printing method to the printed electronics, it is mandatory to increase the resolution of register errors. Therefore it is desired to derive the mathematical modeling of register error or to develop controller design. The cross direction register error was derived considering both lateral motion of moving web and transverse position of printing roll. The mathematical modeling was validated and the relationship between the lateral motion and register error was analyzed by numerical simulations in various operating conditions using multi-layer direct gravure printing machine. The results could be used for a design of the CD register in the multi-layer printing and the lateral motion caused by translation.