In temperate climates, ∼25% of peak elevations in mountain ranges can be created by isostatic rebound as a response to erosional incision. Significantly more relief generation and peak uplift are, however, possible for glacial erosion in a polar climate. We incorporate regional isostasy using flexure of an elastic plate to show that isostatic rebound as a response to glacial incision can account for as much as 2000 m or 50% of peak elevation in the central Transantarctic Mountains. Differences in relief of at least 5500 m over lateral distances of just 40 km are evident within the central part of the 3000-km-long mountain range. Such strong relief is possible because a polar climate since the middle Miocene has resulted in freezing conditions at high elevations, which acted to preserve the peaks, whereas wet-based glaciers at low elevations have produced optimal conditions for enhanced glacial incision. Because isostatic rebound results in permanent peak uplift, this mechanism provides an explanation of why the Transantarctic Mountains are one of the higher and more long-lived continental rift margins on Earth.