Method and core used winding machine

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This method for winding a web material includes : a step for applying an end of the web material (30) onto a damping material (20) formed on the outer peripheral surface of a winding core body (10); and a step for winding the web material around the winding core body while applying tension to the web material. The damping material consists of a soft foam resin, the compressive stress of which at a compressive strain of 20% is 0.02 MPa or lower. The thickness (t1) of the damping material is set to satisfy 0.2 ≥ t2/t1 ≥ 0.1, where t2 is the thickness of the web material. If the compressive stress of the damping material at a compressive strain of α% (20 ≤ α ≤ 60) is σa, and the compressive stress of the damping material at a compressive strain of (α + t2/t1 × 100)% is σb, the relationship of σb/σa ≤6 is satisfied.