A 7mm-08 will work just fine for elk, but within certain parameters.
First, shot placement is very important.
Second, use premium bullets that retain a substantial amount of their weight. Such bullets include - Barnes TSX, Swift-A-Frame, Trophy Bonded Bear Claw, and other similar bullets. If you do not handload, consider Federal's 140 grain Nosler Partition load.
Third, use weights of 140 or more.
Fourth, keep shots as close as possible. I myself would not like to use a 7mm-08 on elks for shots over 200 yards.
Zachary