Various methods of making a reinforced membrane, devices for making the membranes, and the resulting membranes are described. The methods typically provide a reinforcing structure that includes filaments extending around the circumference of the membrane but without the filaments being part of a braided or woven structure. Some of the reinforcing structures also include longitudinal filaments. The methods and devices can be used to make a supporting structure in line with membrane formation steps, and also allow for a reinforced membrane to be produced that has a ratio of inside-to-outside diameters of 0.5 or more.