Winding is one of the major processes in roll-to-roll systems. Taper tension profile in a winding determines the distribution of stress in the radial direction, i.e., the radial stress in the wound rolls. Maximum radial stress is major cause of material defect, and this study has been actively proceeded. Traditional models of radial stress model were focused on flexible and light substrate. In this study, we developed an advanced radial stress model including effects of both these parameters(weight and stiffness) on the radial stress. The accuracy of the developed model was verified through FEM(Finite Element Method) analysis. FEM result of maximum radial stress value corresponds to 99 % in comparison to result with the model. From this study, the material defects does not occur when the steel winding. And steel industry can be applied to improve the winding process.