Boy this is a tougher question than what is big enough for deer. Anything from the 257 roberts up would be better than ok for Elk in my opinion. Bullet construction will depend on a large extent to the caliber being used . Like every other mechanical contraption the skillset of the operator will determine if there is a successful conclusion to the shot. If you can stand the recoil and handle it well then the 300 mag / 338 mag class of cartridges is unbeatable...the 375 will thump them harder but I have never used one on Elk just going on hearsay on this and the track record this great cartridge has. Personally I use a 7 Rem Mag or a 338 and do not think twice about it.