I carry a couple large canvas game bags made to handle one un-boned elk quarter each. One bag will take an average deer if it's boned out. Two will handle the meat from a boned-out elk.
If I am hunting deer, I would probably carry a pack frame to which I could strap the game bag once the meat was packed into it. For elk, you would have a really hard time packing out more than half the meat at one time. [A buddy packed out a young antlerless bull's meat in one trip, but he's exceptionally strong, it was downhill, the truck was close, and that's a rare situation.] For elk, you could hang both bags and come back with horses or an ATV, where legal. I carry a small block and tackle for that task. Otherwise, you'd have to strap one meat bag to your pack frame and hang the other for later retrieval.
That's the less fun part of hunting!
DancesWithKnives