A dual drum winding machine is provided for winding a web of material, e.g., textile material, around a central core. The winding machine is operable on a continuous basis and has a leading winding drum and a succeeding winding drum. The succeeding winding drum is positioned lower than the leading winding drum such that the succeeding winding drum supports a greater proportion of the weight of a forming web roll when the roll is in a winding position supported by both the leading and succeeding winding drums. A method of forming a web roll using the winding machine is also provided.