I hunted elk for the first time last year but I saw everything but elk.
This year I became a Wyoming reason as for hunting as well and got myself general and two leftover cow tags, just to have more options.
During archery season I had no luck, got busted twice. During gun season it started slow but then one evening I saw few cows and calves and was debating should I use any elk tag on them. I decided to give it a go and then realized I will run out legal time by the time I can get a shot. Then the next day I saw them on the opposite side of that valley, about 3/4 of miles away. I kept watching them for 15 mins since there was plenty of legal time left. Then I saw a bull chasing cows and decided to give it a go no matter I have to cross the deep river. Made it on other side of the river and that was much steeper and thicker than it looked from distance. I realized that is a revolver terrain, I won't be able to shoot pass 100 yards anyways. I slowly made my way to opening in the woods, where I saw them last. It took me 15 mins for that final part of the stalk then out of nowhere, I'm stepping out behind one brush and tree and there were 3 cows in front of me at 40 yards, I never saw them. I'm looking quickly, there is no bull in sight. Since it was my first time getting so close to an elk, I lifted my BFR (Big Frame Revolver) in 44 mag, cocked the hammer, picked the smallest elk and let her have it. She was the only one that was looking at me anyway. After first shot they all looked at me and then I gave her one more. Then they started running. She collapsed after 80-90 yards. Found one bullet under hide on the opposite side.
Second elk I was planning to go after when we get enough snow and that happened during Thanksgiving but then I was to tired from my whitetail hunt and didn't use my chance. Week before Christmas I tried again and since snow melted I had to try to find them in the mountain. I found them easily but I only saw bulls and cows I saw too far and to late to be able to get to them before end of legal time. On day before Christmas I decided to go in the afternoon only since morning was beyond cold with crazy winds. I was got to my spot about two hours before sunset and soon after I was getting ready to quit because 29 degrees felt like -10 with that wind. Then I saw one cow at about 1200 yards walking towards me. It's only one but that's all I need. I started making my move towards her and made it about 500 yards when I saw her again coming out small patch of woods. I was at the fence between state and federal land and decided not to shoot from the post, I chose prone instead. Ranged her, she was at 370 and was making her way towards me. It took me time to load my single shot pistol, Remington XP 100 in 6.5 creedmoor, since my fingers were numb. I used my reloads with 127 grain LRX bullets. I knew she will be between 200 and 300 when I get her in my shoe, I just dialed 2 moa found her in my scope and let her have it. She dropped right there. Being the shoulder, full penetration. Exit wound was impressive. It ended up being around 230 yards. Packing out was a challenge. 2.5-3 miles in with 2000 ft elevation gain.