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The in-situ spalling strength (stress at which spallation or, at a larger scale rockburst starts) is reported to be lower than the uniaxial compressive strength obtained in the laboratory; this difference has long been a puzzle. We hypothesise that the spallation is caused by extensive (wing) crack growth parallel to the excavation surface with subsequent buckling of the separated-out rock layers. The wing crack is initiated from a pre-existing defect (crack or pore) under compression. In uniaxial compression such a crack is not capable of extensive growth. In biaxial compression, the intermediate principal stress as low as 5–8.5% of the maximum principal stress was sufficient to make wings sprouting from an initial defect straighten and grow into a large crack comparable to the size of the sample and parallel to the lateral faces of the sample. The intermediate principal stress is invariably present at the excavation wall or face and the biaxial load ratio usually exceeds the critical value, which ensures extensive wing crack growth parallel to the excavation surface and finally spallation. We report new detailed observations of the stages of wing crack growth in biaxial compression. Based on these observations, a model of the wing crack growth and interaction with the free surface (excavation surface) allows relating the spalling strength to the uniaxial compressive strength if the initial cracks causing spallation are sufficiently small. In the case of large initial cracks, the obtained model involves uniaxial compressive strength of the rock mass of the corresponding scale.