Mule deer and elk? Never had the pleasure of shooting something that large. I would recommend something reliable like a bolt action. I hear a .308 is about as small as you want to go. I know a 30-06 will really crack some bones on deer. The heavier the lead and the faster the bullet puts more energy down range. Just pick something that doesn't make you flinch when pulling the trigger. If I were to get a chance at an elk I think my .308 would be fine because it is deadly accurate and not a lot of recoil.