I have never hunted elk, but I have been on my fair share of Moose hunts.
I have seen them take some brutal punishment from a 338 and run 300 yards while sucking up 3 more shots in the kill zone, so yes they are tough, but I have also seen several fall quickly from a well placed shot through the lungs by a 308, 30.06, 7mm mag and 25.06.