High-elevation, low-relief surfaces are widespread in many mountain belts. However, the origin of these surfaces has long been debated. In particular, the southeast Tibetan Plateau has extensive low-relief surfaces perched above deep valleys and in the headwaters of three of the world’s largest rivers (Salween, Mekong, and Yangtze Rivers). Various geologic data and geodynamic models show that many mountain belts grow first to a certain height and then laterally in an outward propagation sequence. By translating this information into a kinematic propagating uplift function in a landscape evolution model, we propose that the high-elevation, low-relief surfaces in the southeast Tibetan Plateau are simply a consequence of mountain growth and do not require a special process to form. The propagating uplift forms an elongated river network geometry with broad high-elevation, low-relief headwaters and interfluves that persist for tens of millions of years, consistent with the observed geochronology. We suggest that the low-relief interfluves can be long-lived because they lack the drainage networks necessary to keep pace with the rapid incision of the large main-stem rivers. The propagating uplift also produces spatial and temporal exhumation patterns and river profile morphologies that match observations. Our modeling therefore reconciles geomorphic observations with geodynamic models of uplift of the southeast Tibetan Plateau, and it provides a simple mechanism to explain the low-relief surfaces observed in several mountain belts on Earth.