I read SA1911s post. I agree. I have killed elk ( a few 0f them) and my wife and several friends have too with my 308. 2 seasons ago my wife and my friend all used the same rifle for their elk and we took 4 of them in 3 days. The 308 I am referring to is a Mossberg MVP with an 18" barrel. It was just fine. The secret is not the gun or the cartridge as much as it is the bullet. Any bullet that will penetrate at least 28" after it expands is fin for elk from about any gun or cartridge.
I prefer to use 165 or 180 grain bullets in my 308 for elk, but as circumstances worked out the rifle was loaded with 150 grain Winchester power points hand loaded my me about 20 years ago for use in some military style 308s I have. The shots were all at about 300-375 yards. Most of those bullets exited. I recovered 2 on the skin of the off side on 2 different elk. Both were quartering shots. One weights 124 grains and one weight 129 grains. Both broke bone.
Magnums and their like are just fine. But that's not to say you need one for elk. I have been hunting and killing elk now for almost 50 years. If you have a bullet that will do it's job you'll be fine.
I have killed elk with three 44 magnum handguns, a 454 Casull handgun, two different 270 Winchesters, one 270 Short mag, one 7X57 Mauser, two 308s, one 30-06, 300 H&H, one 8X57, one 338-06, a 338 mag, a 375H&H, one 62 cal flintlock and one with a wood arrow and single blade broad-head.
I have also seen elk killed by friends, family members and hunters I have guided with 25-06s 257 Roberts, 257 Weatherby mag, 6.5X55, 280 Rem, many 7mm Mags, many 300 Mags, many 30-06s many 270s about ten 308s, 7.65 Belgian, 35 Whelen, 9.3X62s 416 Taylor, 416 Rigby, 45-70s, and one with a 458 Winchester. Add to this list a handful killed with arrows. And I am sure I have missed a few that should be on the list too but that's what I can remember off the top of my head.
The #1 factor in poor kills has been poor bullet placement but the #2 factor is poor bullet construction.
I have seen MUCH better kills from hard cast handgun shots and hard round balls shot from muzzleloaders with hits in the right place than I have from the same placements with poorly made high velocity rifle bullets. And not only a few times either. Poor bullet construction is a big factor in elk rifles. Any bullet that breaks up badly or doesn't exit as a rule, should not be used on elk.
Bullet HOLES kill. Not bullet, not guns, not shell cases. It's the wound that does the job. Use a good bullet and the 308 is a very good elk rifle, (just as most other rifles are too.)