A winding procedure has been developed that results in substantially uniform material properties from the outside diameter to the core of a wound roll of elastomeric webs produced by vertical film lamination (VFL) or stretch bond lamination (SBL) or as registered film. The web material is wound onto the roll in accordance with a wound on tension (WOT) profile that varies with the diameter of the wound web in a manner that was calculated using WOT transposition that is based on a modified version of Hakiel's nonlinear model for wound roll stresses. A constant WOT winding profile is corrected to obtain a compensated WOT winding profile that can be employed to wind the material into a roll that exhibits properties (including MD stress in the web) that are substantially uniform thru-roll. This resulting controlled winding technique has immediate application for webs that are converted for child care products, adult care products, and infant care products.