A tubular membrane includes a support tube made out of one or more flexible tapes of porous support material which have been helically wound into a tube shape with overlapping tape edges which have been sealed to each other, and a semi-permeable membrane layer made of membrane forming material on an inner wall of the support tube. At least one inwardly projecting helical ridge is provided on the inner wall of the support tube, which helical ridge is covered with or forms part of the membrane layer.