An automated system for casting hollow fiber membranes into a variety of prescribed shapes, including spiral, linear, circular and rectangular. The system also has the capability to change the configuration during casting, which increases productivity. A co-extrusion die is rotated over a stationary coagulation bath A computer is used to control the motion of the die to make a membrane with the desired shape The nozzle is oriented in a manner that will compensate for distortions that occur in wall thickness in the area of a bend. In addition, the nozzle's annulus is offset to make the leading portion of the annulus slightly thicker and the trailing portion thinner at the point where the fluids exit the nozzle, which results in a uniformly symmetric wall thickness. A system embodying the invention includes X, Y and .theta.-directional servomotors 1A-1C (FIG. 1), each of which is coupled to an associated position encoder 2A-2C. The motors are controlled by a computer 3 via servodrivers 4 and an associated interface card. Also included in the system are a tub 5 for holding a coagulation bath, bearings 6, carriage 7, screw drive 8, rotary table 9 and co-extrusion die 10.