This invention relates to a method for the production of a coreless roll (110′) including a sheet (110) of flexible, not moist, material such as a fibrous absorbent material, produced by winding of the sheet in one direction and rolling this sheet about a winding axis perpendicular to such direction, and including a central dispensing leader forming a projection along such axis relative to at least one part of the plane of one of the sides of the roll. The method is characterized in that the leader is produced by displacing a portion of the end of the sheet (110) before winding so that one of the longitudinal edges of the sheet forms an angle (α) other than zero relative to such direction of winding, after which winding of the sheet about the axis is initiated. By preference several sheets are produced by longitudinal cutting of a wide sheet. The solution may be applied for production in particular of general wipe rolls, hand towel rolls, or toilet paper rolls.