Mount Muir is a prominent glaciated mountain summit located in the Chugach Mountains, in Chugach National Forest, in the U.S. state of Alaska. Although modest in elevation, relief is significant since the southern aspect of the mountain rises from the sea-level Harriman Fiord of Prince William Sound. The mountain's name was officially adopted in 1910 by the United States Geological Survey, probably after conservationist John Muir (1838-1914) who visited the Alaska area four times, including as a member of the 1899 Harriman Alaska expedition that explored this immediate area.