Elk sometimes do sleep standing up as in taking a nap.
So if the Elk just needs to rest for a little bit then they may be seen during the day sleeping for a little bit standing up.
However when the elk needs to sleep at night they sleep laying down.
To sleep through the night the elk has to lie down to sleep folding their legs under them.
So they will sit down, roll over and pull their legs underneath them.
I've watched an elk go to sleep and I always thought they actually slept standing up but actually they do lay down to sleep.
I've also seen horses lay down at night to sleep although some do sleep in the day standing up.