A method and apparatus for making a cylindrical package in which a cylindrically shaped coil of a long steel strip having a peripheral surface, two end surfaces and a hollow cylindrical center is completely wrapped with a wrapping sheet material so as to have neatly folded closures on both end surfaces with a ring member inserted into the cylindrical hollow center of the coil. At first the wrapping sheet is wrapped around the coil so as to project from either end of the coil by a length l greater than the thickness t between the outermost layer and the innermost layer of the coil. The projecting portions are folded onto the end surfaces by pusher plates with pleat forming rods provided therebetween to form crease lines. The pleated portions of the sheet are flattened onto the folded sheet by the sliding action of pusher plates, and then a ring member is fitted into the cylindrical hollow center of the coil at either end with the edges of the folded sheet pressed underneath so that the wrapping is completed without use of an adhesive.