A method of producing a wound core that is a wound core having a wound shape including a rectangular hollow portion in the center and a portion in which grain-oriented electrical steel sheets in which planar portions (4, 4a) and bent portions are alternately continuous in a longitudinal direction are stacked in a sheet thickness direction, which is a wound core formed by stacking the grain-oriented electrical steel sheets that have been individually bent in layers and assembled into a wound shape and in which the plurality of grain-oriented electrical steel sheets are connected to each other via at least one joining part for each roll, the method comprising: forming at least one of the bent portions of one or more of the laminated grain-oriented electrical steel sheets such that one side of the grain-oriented electrical steel sheet is placed and constrained on a die and a punch is press formed against a portion of the grain-oriented electrical steel sheet to be bent on the other free end side in the thickness direction of the grain-oriented electrical steel sheet, wherein outer surfaces of the die and the punch each have an arc portion (30a, 40a) having a predetermined curvature on a cross section along the thickness direction of the grain-oriented electrical steel sheet, wherein, when the thickness of the grain-oriented electrical steel sheet is T in mm, bent angles of the bent portions are θ in °, a radius of curvature of the arc portion of the die is Rd in mm, and a radius of curvature of the arc portion of the punch is Rp in mm, relationships of Equations to below are satisfied, and wherein the portion of the grain-oriented electrical steel sheet to be bent is pressurized by the arc portion of the punch and bent along the arc portion of the die so that four or more of the bent portions are formed in one of the grain-oriented electrical steel sheets. 0.02 ≤ T / 2 Rd + T ≤ 0.15 0.5 ≤ Rd ≤ 3.0 0.15 ≤ T ≤ 0.30 2.5 ≤ Rp / Rd ≤ 10 10 ° ≤ θ ≤ 90 ° forming at least one of the bent portions of one or more of the laminated grain-oriented electrical steel sheets such that one side of the grain-oriented electrical steel sheet is placed and constrained on a die and a punch is press formed against a portion of the grain-oriented electrical steel sheet to be bent on the other free end side in the thickness direction of the grain-oriented electrical steel sheet, wherein outer surfaces of the die and the punch each have an arc portion (30a, 40a) having a predetermined curvature on a cross section along the thickness direction of the grain-oriented electrical steel sheet, wherein, when the thickness of the grain-oriented electrical steel sheet is T in mm, bent angles of the bent portions are θ in °, a radius of curvature of the arc portion of the die is Rd in mm, and a radius of curvature of the arc portion of the punch is Rp in mm, relationships of Equations to below are satisfied, and wherein the portion of the grain-oriented electrical steel sheet to be bent is pressurized by the arc portion of the punch and bent along the arc portion of the die so that four or more of the bent portions are formed in one of the grain-oriented electrical steel sheets. 0.02 ≤ T / 2 Rd + T ≤ 0.15 0.5 ≤ Rd ≤ 3.0 0.15 ≤ T ≤ 0.30 2.5 ≤ Rp / Rd ≤ 10 10 ° ≤ θ ≤ 90 °