The present invention improves accuracy in the axial dimension of rolled parts for a chain such as bushings, rollers and similar. A rolled part is manufactured by cutting a strip of steel into a rectangular shape to obtain a rectangular base material having a predetermined dimension, The rectangular base material is rolled into a clindrical shape to obtain a cylindrically formed part having cut end surfaces face each other. A core is inserted for rolling the rectangular base material into the cylindrically formed part. The cylindrically formed part is then pressed through a die having a circular opening. The rolled part has a plurality of blind grooves on a surface thereof. While the cylindrically formed part is being pressed through the die having a circular opening, a plastic flow of the material of the cylindrically formed part intensively occurs in a direction toward the blind grooves. Since the plastic deformation of the rolled part is absorbed by the blind grooves, axial dimension of the rolled part hardly varies,