From 2003 to 2007, eruptive activity at Piton de la Fournaise was shown to follow cycles, comprising many summit/proximal eruptions and finishing by a distal eruption. GPS measurements evidenced striking asymmetric deformation between its western and eastern flanks. Horizontal displacements recorded during interdistal periods showed a characteristic amplitude at the top of the eastern flank. Displacements recorded at the base of the summit cone showed a bimodal distribution, with low amplitudes during interdistal periods and large ones during distal eruptions. To account for displacement asymmetry, characteristic amplitude, and large flank displacement, we modeled the volcanic edifice using a Drücker-Prager elastoplastic rheology. Friction angles of 15° and >30° were needed to model the displacements respectively during distal eruptions and interdistal periods; this change shows that strain weakening occurred during distal events. Large plastic displacement that occurred in the eastern flank during distal eruptions relaxed the horizontal elastic stress accumulated during interdistal periods; it triggered summit deflation, horizontal magma transfer, and distal flank eruption and reset the eruptive cycle. Our elastoplastic models also show that simple source geometries may induce large eastern flank displacements that would be explained by a complex geometry in a linear elastic edifice. Magma supply is often thought to control volcano's eruptive activity, with surface deformation reflecting changes in magma supply rate, the volcano's response being linear. Our results bring some evidences that on Piton de la Fournaise time-space discretization of magma transfer may be the result of the edifice's nonlinear response, rather than changes in magma supply.