A method includes: providing a plate-like glass element having side faces and an ultrashort pulse laser having a laser beam; directing the laser beam onto one of the side faces; concentrating the laser beam by focusing optics to form an elongated focus in the glass element; producing a filament-shaped flaw in a volume of the glass element by a radiated-in energy of the laser beam, a longitudinal direction of which runs transverse to one of the side faces, and the ultrashort pulse laser radiates in a pulse or a pulse packet having at least two successive laser pulses to produce the filament-shaped flaw; widening the filament-shaped flaw to form a channel by exposing the glass element to an etching including an etching medium which removes glass at a rate of less than 8 μm per hour; and introducing rounded, hemispherical depressions in a wall of the channel by the etching.