Abstract: Prosthetic vessels having improved resistance to occlusion by tissue reaction upon implantation by reducing transmural stresses are also disclosed. Prostheses having elliptical cross-sections governed by the maximum strain expected in the natural vessel and possessing a higher bulk compliance than previous designs are provided. Additionally, novel methods are presented for implanting improved prostheses by using angled bias cuts to produce an elliptical cross-section at each end of the natural vessel section receiving the prosthesis. In accordance with preferred embodiments, vessels are provided where the cross-sectional geometry is approximated by the equations:a=r.sub.0 [1+2.epsilon. (2+.epsilon. )].sup.1/2andb=r.sub.0.

Abstract: Methods for attaching prostheses to natural vessels are disclosed. Prosthetic vessels having improved resistance to occlusion by tissue reaction upon implantation by reducing transmural stresses are also disclosed. Prostheses having elliptical cross-sections governed by the maximum strain expected in the natural vessel and possessing a higher bulk compliance than previous designs are provided. Additionally, novel methods are presented for implanting improved prostheses by using angled bias cuts to produce an elliptical cross-section at each end of the natural vessel section receiving the prosthesis. In accordance with preferred embodiments, vessels are provided where the cross-sectional geometry is approximated by the equations:a=r.sub.0 [1+2.epsilon.(2+.epsilon.)].sup.1/2andb=r.sub.0.