Nonbreeding individuals regularly land at many points, including coastal Antarctica. The annual life cycle involves lengthy stays at sea alternating with periods ashore for breeding, molting, and resting. Immature individuals, along with females that have not recently given birth, come ashore to molt from November to January. May. Molting takes 3-40 days, and the animals do not feed during this period. They then go to sea again, returning to the breeding grounds in August or September.
Preferred beaches are flat and smooth, with a substrate of sand, rounded stones, or pebbles.
Some animals move into areas of tussock grass, and molting females often seek muddy wallows. Like M. angustirostris, M. leonina has flexible flippers and sometimes scoops sand over itself to lower body temperature. At the southern edge of its range, M. leonina hauls out on snow or ice. It can make access holes by butting though the ice with its head, and it may travel 20 km under the ice, utilizing air pockets along the way. It is capable of long, deep dives and has been known to remain underwater for over 30 minutes.