A method and apparatus provided for the production of fine fibers by electrospinning fibers by applying an electrical field between a primary electrode and a counter electrode (5) spaced apart from the primary electrode and extending generally parallel thereto wherein at least an operative surface of the primary electrode is coated with a polymer solution (3) and an electric field of sufficient magnitude is generated between the primary electrode and counter electrode to cause the formation of fine fibers (9) in the space between the electrodes. The operative surface of the primary electrode that is coated with polymer solution is made up of appropriate portions of the surfaces of a multitude of operatively semi-submerged, loose (unattached) elements (1, 11, 17, 21) supported on the bottom of a trough (2) or tray or another support member or members (12, 18, 22). Facility is included for causing polymer solution to be applied to the exposed surfaces of the loose elements by causing them to roll in the polymer solution so that they become coated with a thin layer of polymer solution on their surfaces.