I have been hunting elk and guiding hunters for most of my life, and I am getting to be an old man. Funny thing is that in all the years I have hunted and guided, I have never seen an elk shot with a 264 Mag.
I have seen them killed with 6.5X55, 6.5-06 and 260 Remingtons. What I can tell you is that all 3 of the above shells mentioned work fine if the bullets hold together.
But driving a bullet faster can make it come apart a lot worse, so my best guess would be to use a bullet of 140 or heavier, and get a Nosler Partition, Swift A-frame, any bonded or any expanding solid, and you'll be fine.
Stay away from any bullet that weights less then 60% of it's unfired weight when it stops.
The 264s I have seen used were all used against mule deer, and I can tell you that they were accurate and had a LOT of range, so I am sure you'll be fine using one on elk, as long as you shoot "elk bullets", not target bullets or any bullet that comes apart and completely sheds it's jacket.
