Most folks tend to agree on a .270 Winchester/.280 Remington as being a relatively noncontroversial/acceptable minimum, with a .30-06 being a bit better due to it's caliber and projectile weight/selection, a 7 mm Rem Mag perhaps a bit better yet due to it's velocity/range, then perhaps a .300 WinMag, with a strictly primary elk rifle perhaps culminating in the .338 Win Mag chambering. (The middle of the road classics are probably the .30-06/.300 win) Certainly better to choose an -06 that can be handled/shot well, than a flinch-inducing non-ported 7 lb .340 Weatherby with 5 times the felt recoil.

A few folks will vote for a bit above and a bit below these power/caliber/momentum levels, but, to each his or her own. It's your hunt, and good luck!