Elk drop pretty late, any where from mid March till late April. I hunted turkeys in the Black Hills in mid April and have seen spike bulls still carrying. My kids and I found 4 sheds in June (three 6pts and a 5pt). You can see them form along ways away. Have fun!
Usually around the first week of April I will strap my snowshoes to my pack and head into the high country to look.
Most of the big bulls start dropping here in late March, into early April being the most concentrated drop. Young bulls will pack into May..