For years, we had driven US50 between Montrose and Gunnison, seeing this mountain and its very noticeable flat, north-sloping summit ridge. It can be spotted from many miles away by this distinct shape. For a long time, we were unaware that this was a ranked 13er.
Begin this hike from the trailhead located at the sharp switchback on FR864, a half mile south of the camp area and trail crossing of the Alpine Trail. The hiking here is easy and gentle, following an old roadbed for 1.5 mile to a crossing of the Little Cimarron over to the west side. There will likely be no assist here to cross. Continue hiking south another 1.5 mile still following the old roadbed that will dwindle to a trail. At about 3.0 miles in on this hike, you will be east of the northern flat summit ridge of Sheep Mountain. To this point, most of the hiking has been well forested. There is a now series of five distinct avalanche chutes that sweep down off the east face of the mountain. Count these chutes and when you come to the fifth, that's where you can head up to the west. By then, you will be almost directly east of and below the summit. This particular chute is distinguished from the others by having an "island" of trees in the middle of the chute that have survived. There are also two drainages within this chute. Google Earth shows the trail well up on the hillside here, above the creek. Coordinates for this chute are: N 38° 09' 43.68 W 107° 26' 59.48".
Head west, hiking up this chute which will steepen as you gain elevation. You will be hiking through low conifers, avalanche debris and farther up, lush grass and tundra. When we did this hike, there was abundant evidence of elk grazing in this area. Most of your elevation gain for the day will be in this stretch - around 2,400 feet. As you near the summit, it's probably easiest to swing a little more south to avoid some cliffs below the summit, following on the south side of a ridge of sorts to emerge on the summit plateau just south of the true summit. The lush tundra will have given way to low tundra and smaller embedded scree and rocks. Once you arrive here, take a look at the view into the East Fork of the Cimarron far below.
The view into the East Fork of the Cimarron is astounding from here. As one can see on the map, the entire western flank of Sheep Mtn. is an intricate convolution of eroded rock worn into fantastic cliffs, spires, gullies and indescribable forms. It's really indescribable. From this summit, either return as you came or continue on to UN 13,100.
Additional Note: It is also possible to begin this hike from the primitive camp area a half mile north of the switchback/trailhead, where the Alpine trail can be accessed. There is a bridge across the creek here to take hikers to the west bank. Hike south on a good trail until you come to an intersection. Take the lower trail (left) and continue hiking south up along the creek. At times, this trail may fade in grassy, open sections, but press on. After 2 miles, it will intersect the main trail where it crosses over from the east side of the Little Cimarron. From there, on, the route is as described above.
Links to other information, routes & trip reports for this peak that may be helpful.