The aim of this study was to identify the influence of specimen geometry and size on the results of aortic uniaxial tensile tests using custom-designed tissue cutters, clamps and molds. Six descending thoracic aortas from pigs were used for rectangular sample tests, in which the circumferential and axial specimens had widths of 6 mm, 8 mm and 10 mm. The other six aortas were used for the dog-bone-shaped sample tests and were punched into circumferential, axial and oblique specimens with widths of 2 mm, 4 mm and 6 mm. We performed uniaxial tensile tests on the specimens and compared the test results. The results showed that mid-sample failure occurred in 85.2% of the dog-bone-shaped specimens and in 11.1% of the rectangular samples, which could be caused by Saint-Venant’s principle. Therefore, rectangular specimens were not suitable for aortic uniaxial tensile testing performed until rupture. The results also showed that the size effect of the aorta conformed to Weibull theory, and dog-bone-shaped specimens with a width of 4 mm were the optimal choice for aortic uniaxial tensile testing performed until rupture.