Provided are a method and apparatus for manufacturing a wound body in which nonuniformity of width is suppressed when a roll of material is laid out. A wound body manufacturing apparatus (1) is provide with a stretching device (30) for stretching a long, thin film (Rp) of a viscoelastic body, a cutting means (55) for cutting the stretched film (Fp) to a predetermined width, a tension roller (52) for applying longitudinal tension to the film (Fp) cut by the cutting means (55), a winding device (60) for winding the cut film (Fb), and a controller (90). The film (Fp), when cut, is cut while the tension applied to the film (Fp) in the longitudinal direction is varied. The width of the cut film (Fb) can be varied according to the tension, and when a predetermined amount of time has elapsed with the cut film (Fb) in a wound state, it is possible to suppress nonuniformity in the width of the film (Fb) due to the position where the film (Fb) is wound.