Use a good bullet and place it well. Elk are tough, but if you wait for a good shot and use a good bullet they will fall.
I have only ever really hunted cow elk, but I have started moving from less tough bullets to tougher bullets especially since I have started hunting country that can be thicker vegetation. Even with good shots elk can run, and if they get in the weeds having a tougher bullet that creates an exit wound helps with a blood trail.
I have shot most of my cows with .257 or 6.5 cal Berger bullets until my last hunt when I used a 30 cal Barnes TTSX. I am starting to switch back to the heavier bullets in heavier calibers camp, but it isn't a requirement. My group killed 3 cow elk last hunt. The first was a big cow with 6.5x55 and 135gr Berger Classic Hunter, not a big tough bullet, but it was a clean double lung. Thankfully the Berger created an exit wound which they normally haven't from my experience, because the cow ran in some thick stuff and even with some blood trail it took a little while to find her. The next 2 were shot with Barnes TTSX 165 and 168gr. The first was a 308 win, and that cow dropped like a stone. The 2nd was a 300 weatherby mag and that cow ran 40yards or so.
The longest kill I have on a cow elk though is only about 270 yards and was with the smallest bullet I have used which was a 257 weatherby mag and Berger 115gr HVLD. She went 40 yards. I did shoot her twice, but to me if an elk is standing I am going to keep shooting. The first shot was a clean double lung, she would have fallen, but if she ran it would have been harder to get her out.