Historically wound roll models have required the input of a radial modulus of elasticity. Heretofore this modulus has been measured using material testing systems which have shown the radial modulus to be dependent upon radial pressure and that it is typically much less than the in-plane moduli of the web. This paper focuses upon a method in which the radial modulus can be predicted based upon surface roughness characteristics. The advantage of this method is that wound roll stresses can be predicted prior to the manufacture of the web. Thus winding strategies can be developed prior to the production of the web. An application of this theory will be presented on polymer webs with experimental verification.