The Wound-On-Tension (WOT) is the tension in the outermost lap of a winding roll during winding. It is the most influential input that determines the wound roll stresses. WOT is dependent of winder types, material properties of web, winding parameters, and geometry of winders. We developed an explicit model to account for all those aspects. Winder types of pure center winder, center winder with nip, surface winder, and hybrid winder were studied. Web material properties are known to be state dependent. This is accommodated by implementing a user subroutine VUMAT in Abaqus. New test methods were developed for out-of-plane shear modulus. Experimental verifications of the WOT were conducted and good agreement was found. A parametric model was developed by Python scripts, which facilitates use of the model by other analysts.