To understand the volcano-tectonic history of Piton des Neiges (the dormant volcano of La Réunion), we measured in the field the orientation of sheeted intrusions and deformation structures, and interpreted the two datasets separately with a paleostress inversion. Results show that the multiple proposed rift zones may be simplified into three trends: (1) a N30°E, 5 km wide linear rift zone running to the south of the edifice, active in the shield building (≥ 2.48–0.43 Ma) and terminal stages (190–22 ka); (2) a curved N110 to N160°E rift zone, widening from 5 km to 10 km toward the NW flank, essentially active during the early emerged shield building (≥ 1.3 Ma); and (3) two sill zones, ≤ 1 km thick in total, in the most internal parts of the volcano, active in the shield building and terminal stages. In parallel, deformation structures reveal that the tectonics of the edifice consisted in three end-member stress regimes sharing common stress axes: (1) NW-SE extension affecting in priority the south of the edifice near the N30°E rift zone; (2) NNE-SSW extension on the northern half of the volcano near the N110-160°E rift zone; (3) compression occurring near the sill zones, with a NE-SW or NW-SE maximum principal stress. These three stress regimes are spatially correlated and mechanically compatible with the injection trends. Combined together, our data show that the emerged Piton des Neiges underwent sector spreading delimited by perpendicular rift zones, as observed on Piton de la Fournaise (the active volcano of La Réunion). Analogue experiments attribute such sector spreading to brittle edifices built on a weaker substratum. We therefore conclude that La Réunion volcanoes are both brittle, as opposed to Hawaiian volcanoes or Mount Etna whose radial spreading is usually attributed to a ductile body within the edifices.