Pressure-temperature-time paths obtained from minerals in metamorphic rocks allow the reconstruction of the geodynamic evolution of mountain ranges under the assumption that rock pressure is lithostatic. This lithostatic pressure paradigm enables converting the metamorphic pressure directly into the rock's burial depth and, hence, quantifying the rock's burial and exhumation history. In the coherent Monte Rosa tectonic unit, Western Alps, considerably different metamorphic pressures are determined in adjacent rocks. Here we show with field and microstructural observations, phase petrology and geochemistry that these pressure differences cannot be explained by tectonic mixing, retrogression of high-pressure minerals, or lack of equilibration of mineral assemblages. We propose that the determined pressure difference of 0.8 ± 0.3 GPa is due to deviation from lithostatic pressure. We show with two analytical solutions for compression- and reaction-induced stress in mechanically heterogeneous rock that such pressure differences are mechanically feasible, supporting our interpretation of significant outcrop-scale pressure gradients.