Flat membranes from foils of organic polymers, glass or ceramic materials have pores tapering in funnel-shaped fashion, with a fixed pore size and a pore size distribution of less than 10% and an arrangement of the pores in a pattern of adjacent rows, wherein the average pore diameters range from 0.05 to 10 .mu.m and the pore patterns are evenly arranged in a regularly bounded area and, between the individual pores, have remaining webs with varying heights in the plane parallel to the increase in thickness of the foil material. It is manufactured through erosion of the pores by use of one or more intensity-modulated laser beams and continuous transport of the foil past the laser or lasers, with a pulse duration ranging from 1 to 1000 ns.