A ureter prosthesis fabricated from copolyurethane materials which are non-reactive in the urinary environment and adapted for fixation within a patient to avoid adverse migration. This ureter prosthesis can be adapted for intermediate location along a ureter or can be constructed with one-way valve means appropriate for implantation into the bladder lumen without a resulting vesico-ureteral reflux. The ureter prosthesis includes an elongate duct having a lumen whose interior surface is ultrasmooth based on microscopic inspection. An exterior cuff with terminal and intermediate sewing projections is formed around a portion of the elongate duct to enable its fixation by suturing to appropriate muscular tissue. The utility and success of this ureter prosthesis has been confirmed in multiple testing of dogs which have survived more than a year with the prosthetic ureter in place.