10 Bears, a 180g Hornady BTSP or flat base would be a much better bullet in case you hit a shoulder or heavy rib, I can't say enough good about these two bullets as I learned shooting hogs.
So you know, elk are not hard to kill, it is all about bullet placement. I killed 8 with a 7x 57 loaded with 140g Sierra sp flat base when I did not know any better. Then went to a 7 mag with the new 140g Nosler ballistic tips, killing two large bulls.
Neither of these calibers and bullets that I killed elk with would be considered adequate today, but this was 35 years ago when I was in my very early 20's.
With all those elk we killed, I never saw anyone hit one on the shoulder. I skinned and butchered all my animals, and am very leary of using any caliber or bullet to hit a shoulder intentionally. I got lucky many times and hit the animals mid body where they collapsed at a dead run.
I have a friend that has killed 50+ elk with a 300 WM with 180g Sierra BTSP, which is also a bullet on the tad softer side vs the Hornady BTSP.
The bullet is the cheapest part of the hunt. Today if I were going elk hunting, I would use a Heavy for caliber Nosler Partition as it would break shoulders and hips and keep on going. We got real lucky on those running elk, but we were shooting a lot of jack rabbits on the run at that time. What is very deceiving is that an elk is very big, when it is running, it does not look to be moving very fast, so you have a tendency to not leade it as much as you should. You may find yourself thinking that you would not shoot one on the run, but if you jump one in a clear cut that looks like he has an oak tree on his head, you will take a shot or three! You have to discipline yourself to not look at the rack!
Elk like to bed down in clear cuts, on the sunny side. We walked these clear cuts, a guy on each side and one in the middle. We had good success many times. Taking a shot up the Azz on a full grown elk is not a good idea, but the Nosler partition would get the job done in spades.