The umbilical cord contains blood vessels that supply nutrients and oxygen during gestation. Maintaining patency and vasoregulatory capabilities in these vessels is critical for allowing normal growth in utero. Yet, at birth, the umbilical arteries close within seconds, while the umbilical vein remain open, leading to a transfusion of placental blood that allows for better health of the newborn. We investigated the structure-function relationship of the umbilical arteries and veins using biomechanical modeling, which suggested that the structural dimorphism between these vessels is key in allowing for the closure of the umbilical artery at birth. Indeed, the structure of the artery allowed for buckling instabilities to develop with layer-specific contraction of smooth muscle cells, while the structure of the umbilical vein inhibited this closure mechanism.