Mount Bear is a high, glaciated peak in the Saint Elias Mountains of Alaska. It lies within Wrangell-Saint Elias National Park, about 4 miles west of the Yukon border. The Barnard Glacier flows from its southwest slopes, while the Klutlan Glacier lies to the north. Its principal claim to fame is that it is a fourteener, and in fact one of the highest 20 peaks in the Uniteā¦Mount Bear is a high, glaciated peak in the Saint Elias Mountains of Alaska. It lies within Wrangell-Saint Elias National Park, about 4 miles west of the Yukon border. The Barnard Glacier flows from its southwest slopes, while the Klutlan Glacier lies to the north. Its principal claim to fame is that it is a fourteener, and in fact one of the highest 20 peaks in the United States.