Chronic hypoxia during gestation and postnatal period induces pulmonary hypertension, aorta stiffening and vascular remodeling. In this study, we hypothesized that a postnatal treatment with Cinaciguat, a guanylate cyclase activator, may improve the vascular function by enhancing NO-sGC pathways that induce vasodilation. To assess this, we collected aortas from six lambs gestated, born and raised at 3600 masl. Half of these lambs received a Cinaciguat postnatal treatment, while the other half was used as control (vehicle). Uniaxial tension was applied on samples of each group of aortas (control and Cinaciguat-treated) through cyclic loading. The obtained stress–stretch curves were used to identify constitutive parameters of a hyperelastic damage model. These material constants allowed us to assess the softening/dissipation behavior and to characterize the treatment effects. Results showed that Cinaciguat has an effect on the damage behavior at large strains, altering the damage onset under uniaxial tension. We conclude that Cinaciguat, as a vasodilator, can prevent the very early effects of vascular remodeling caused by perinatal hypoxia, and improve the aortic-tissue damage properties of hypoxic lambs.