A vascular prosthesis is constructed from a structure having interconnected, helically oriented channel-porosity to allow oriented ingrowth of connective tissue into a wall of the prosthesis. The prosthesis can have a small internal diameter of 6 mm or less. Several different methods can be used to produce the prosthesis, including a fiber winding and extraction technique, a melt extrusion technique, and a particle and fiber extraction technique using either a layered method or a continuous method. Furthermore, mechanical properties of the prosthesis are matched with mechanical properties of the host vessel, thereby overcoming problems of compliance mismatch.