Bedrock stresses induced through exhumation and tectonic processes play a key role in the topographic evolution of alpine valleys. Using a finite difference model combining the effects of tectonics, erosion, and long-term bedrock strength, we assess the development of near-surface in situ stresses and predict bedrock behavior in response to glacial erosion in an Alpine Valley (the Matter Valley, southern Switzerland). Initial stresses are derived from the regional tectonic history, which is characterized by ongoing transtensional or extensional strain throughout exhumation of the brittle crust. We find that bedrock stresses beneath glacial ice in an initial V-shaped topography are sufficient to induce localized extensional fracturing in a zone extending laterally 600 m from the valley axis. The limit of this zone is reflected in the landscape today by a valley “shoulder,” separating linear upper mountain slopes from the deep U-shaped inner valley. We propose that this extensional fracture development enhanced glacial quarrying between the valley shoulder and axis and identify a positive feedback where enhanced quarrying promoted valley incision, which in turn increased in situ stress concentrations near the valley floor, assisting erosion and further driving rapid U-shaped valley development. During interglacial periods, these stresses were relieved through brittle strain or topographic modification, and without significant erosion to reach more highly stressed bedrock, subsequent glaciation caused a reduction in differential stress and suppressed extensional fracturing. A combination of stress relief during interglacial periods, and increased ice accumulation rates in highly incised valleys, will reduce the likelihood of repeat enhanced erosion events.