If you really wanted to you could kill an elk with a .22, so a .308 will work fine. People I hunt with have killed several elk with the 7mm/08 (.308 necked down for 7mm bullets) using plain jane 140 gr. Winchester Super X ammo. And most of the guys I hunt with have used .270's and 30-06's with cheap 150gr bullets for over 30 years and killed elk almost every year with no probelms. I also know people who have killed elk using a .243. Just place your shots in the kill zone. Regardless of how big of a gun you're using, if you make a bad shot the elk won't go down.