The ski resort town of St Moritz, Switzerland, is partially constructed on a large creeping landslide, which has been causing damage to buildings and infrastructure. At the town centre, the landslide is constrained by a rock outcrop, creating a compression zone in the sliding mass. After decades of gradual slowing down,s in the beginning of 1990s the landslide started to accelerate, in spite of the fact that the average yearly precipitation and the pore water pressure on the sliding surface remained fairly constant. The paper shows that a constrained creeping landslide experiences progressive failure caused by the propagation of a zone of intense shearing along the slip surface resulting in significant earth pressure increase and visco-plastic yielding of soil in the compression zone. This basic physical mechanism, relying on extensive laboratory and field tests and long-term displacement monitoring, explains the paradox of the St Moritz landslide acceleration. Although the model predicts that the landslide could eventually slow down, its displacements may become excessive for some buildings, requiring an early warning system and further stabilization of the historic Leaning Tower. In general, by predicting the onset of yielding, the model can provide an important timeframe for stabilization of constrained landslides.