A hollow fiber membrane is formed by embedding a braid having a spiral open weave of monofilaments only, to avoid a “whiskering” problem common in prior art multifilament braid-supported tubular membranes. The open weave is characterized by contiguous, circumferential, rhomboid-shaped areas of polymer film separated by monofilaments. When the braid is supported on a plasticized PVA cable it can be infiltrated with membrane polymer which, when coagulated embeds the braid positioning it around the lumen. The spiral weave, free of any circumferentially constricting monofilament, when embedded in film, allows the membrane to be biaxially distensible. In other words, the membrane has “give” not only in the axial or longitudinal direction but also in the radial direction. “Give” in the radial direction permits soiled membranes to be backwashed under higher pressure than in a comparable braid which is not radially distensible.