Abstract The relationship between the mechanical properties of a fibrous polyurethane arterial prosthesis and the graft manufacturing process variables was studied from uniaxial tensile tests. A non-linear model was used to characterize the cylindrical elastic properties. Experiments on cylindrical segments were carried out to determine the constitutive constants and to assess the applicability of the model to the polyurethane graft. The compliance of 4 mm internal diameter grafts with various wall-thicknesses was predicted. The results were used to produce grafts with compliance matched to that of the carotid and femoral arteries.