So where DO you take that shot? No question, the brain or heart shot no matter the bullet, and it's over. However, don't try it. First choice is always, for all large game, the double lung shot first. For the Elk, it's the neck second. If you are going to pull a shot one way or the other, go for the neck, not the gut. A gut shot and the elk, deer or antelope etc... will run 5 miles, even with the end trails hanging out.
With Elk, the double lung shot with heavy penetration and exit as you get with a Nosler Partition is always your first choice. Last year, I was underpowered with a 25-06 but with a 115 grain Partition, a moving target, almost 300 yards and I pulled the shot just off the front of the lungs to the base of the neck. She dropped faster than any game I've ever taken (other than a doe at 50 yards with my .458 win mag sporting a 510 grain soft point which hit the ground so hard it bounced).
Check out this photo and get an idea of just how big the lung and neck area is:
Just ask if you have question about penetrating bullets etc.... Federal Premium Ammo, Nosler Partition bullets - consider it - do it.