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International audience; Field work carried out on the Piton des Neiges volcano (Réunion Island) suggests that the injection of magma along detachments could trigger flank failure by conjugate opening and shear displacement. We use 3-D numerical models to compare the ability of purely opened sheet intrusions, sheared sheet intrusions, and normal faults to induce flank displacement on basaltic volcanoes. We assume that shear stress change on fractures results from stress anisotropy of the host rock under gravity. Exploring a large range of stress anisotropies, fracture dips, and fracture depth over length ratios, we determine that the amount of shear displacement is independent of the proximity to the ground surface. Sheared sheet intrusions are the most efficient slip medium on volcanoes. Consequently, the largest flank displacement is induced by the longest, deepest sheared intrusion dipping closest to 45° in a host rock with the highest stress anisotropy. Using our model in a forward way, we provide shear and normal displacements for buried fractures. Applying the model to a pile of sills at the Piton des Neiges volcano, we determine that the mean shear displacement caused by each intrusion was 3.7 m, leading to a total of a 180–260 m of lateral displacement for the 50 m high pile of sills. Using our model in an inverse way, we formulate a decision tree to determine some fracture characteristics and the host rock stress anisotropy from ratios of maximum surface displacements. This procedure provides a priori models, which can be used to bound the parameter space before it is explored through a formal inversion. Applying the decision tree to the 1.4 m coeruptive flank displacement recorded at Piton de la Fournaise in 2007, we find that it probably originated from a shallow eastward dipping subhorizontal normal fault.