I use a .300 Win Mag for elk. I'm old and small, but I really like my .300 Win Mag with Nosler 180 gr Protected Point Partition bullets (handloads sighted 2.5-2.75" high at 100 yards.) Generally I'd recommend a .30-06 for most hunters, or a 7mm Rem Mag. A .270, .280, or .308 will certainly kill any elk but I prefer a flatter shooting long range cartridge when I face the expense of an outfitted elk hunt.
NRA Life Member - RMEF Life Member - Vietnam Vet