A method for producing a cavity in a substrate composed of hard brittle material is provided. A laser beam of an ultrashort pulse laser is directed a side surface of the substrate and is concentrated by a focusing optical unit to form an elongated focus in the substrate. Incident energy of the laser beam produces a filament-shaped flaw in a volume of the substrate. The filament-shaped flaw extends into the volume to a predetermined depth and does not pass through the substrate. To produce the filament-shaped flaw, the ultrashort pulse laser radiates in a pulse or a pulse packet having at least two successive laser pulses. After at least two filament-shaped flaws are introduced, the substrate is exposed to an etching medium which removes material of the substrate and widens the at least two filament-shaped flaws to form filaments. At least two filaments are connected to form a cavity.