Precipitation runoff from the mountain's north slope drains to the Yellowstone River via Tom Miner Creek, whereas the south slope drains to Specimen Creek which is a tributary of the nearby Gallatin River.

Topographic relief is significant as the summit rises approximately 1,800 feet (549 meters) above headwaters of North Fork Specimen Creek in one mile (1.6 km).

The mountain's toponym has been officially adopted by the United States Board on Geographic Names.

[3] This peak should not be confused with the other Sheep Mountain also in Park County, Montana, but in the Absaroka Range.

Based on the Köppen climate classification, Sheep Mountain is located in a subarctic climate zone characterized by long, usually very cold winters, and mild summers.