The study of the mechanical properties of swine carotids has clinical relevance because it is important for the appropriate design of intravascular devices in the animal trial phases. The inelastic properties of porcine carotid tissue were investigated. Experimental uniaxial cyclic tests were performed along the longitudinal and circumferential directions of vessels. The work focused on the determination, comparison, and constitutive modeling of the softening properties and residual stretch set of the swine carotid artery over long stretches and stress levels in both proximal and distal regions. It was observed that the residual strain depends on the maximum stretch in the previous load cycle. The strain was higher for distal than for proximal samples and for circumferential than for longitudinal samples. In addition, a pseudoelastic model was used to reproduce the residual stretch and softening behavior of the carotid artery. The model presented a good approximation of the experimental data. The results demonstrate that the final results in animal trial studies could be affected by the location studied along the length of the porcine carotid.