The focus of this study is on the development of a mathematical model for estimating tension of a printing section by using the register error in R2R (Roll to Roll) e-Printing systems. In a printing section of conventional R2R printing systems, the tension is generally measured not for controlling but for monitoring, because the tension control may cause the occurrence of a register error. But, for high precision control, the tension in the R2R e-Printing system must be controlled as well as measured for more precise control of the register error. The tension can be measured by the loadcell in the conventional R2R systems. However, installing a loadcell on the R2R systems causes extra economic burden. In addition, the space for adding a loadcell on R2R systems is limited due to many components including dryers, lateral guider, doctor blade, ink supply unit and cooling unit. Therefore, a tension estimator can be another possibility for predicting the tension in a printing section. In this study, a new tension estimation model is proposed. The proposed model is based on the register error model, the equivalent torque equation, and the tension model considering tension transfer. Numerical simulations and experimental results showed that the proposed model was effective in estimating the tension in a printing section.