This study presents a continuum analysis of a simple pressurized cylindrical shell geometry relating to a problem of potential interest in biomedical engineering. Repair or partial replacement of veins by adhesive splicing rather than suturing involves an evaluation of the strength of the joint, especially at the ends where the prosthesis slips over or into the natural vein. Furthermore, the quality of the adhesive bond may change with biodegradability of the joint. The analysis suggested may be used either to deduce the specific adhesive fracture energy(γa)of the bond or to assess its mechanical integrity in pulsatile flow, providing an independent measurement of the energy(γa)has been made.