The mountain is located some distance from Shining Time and the Indian Valley and according to the 1999 script, it muffles all train whistle sounds coming from the valley, which is the reason Burnett moved to the mountain. It also has a station on the Indian Valley Railroad.
Trivia
The Muffle Mountain scenes were filmed on Dalby Mountain in the Isle of Man.
Burnett Stone's workshop for Lady is located inside the mountain.
P.T. Boomer tried blasting with dynamite into the mountain to find Lady in the original cut of Thomas and the Magic Railroad.