The invention is a method for structuring a flat substrate composed of glass material in the course of a viscous flow process. The glass flat substrate is joined to a surface of a flat substrate, which is preferably a semiconductor flat substrate, having at least one depression bounded by a circumferential edge located in the surface. In the course of a subsequent tempering process, glass material is changed to a viscous free-flowing state in which at least proportions of the free-flowing glass material of the flat substrate flow over the circumferential edge into the depression in the flat substrate. The invention is also characterized in that a flat substrate is provided of which the at least one depression has at least one wetting surface that is countersunk with respect to the surface of the flat substrate and is at least partly bounded by a line-type edge which, at the same time, is an edge of a trench structure provided within the depression and countersunk with respect to the wetting surface and/or is determined by a discontinuous change in a wetting property for the free-flowing glass material that can be assigned to the wetting surface.