Identifying the causes of flank destabilization of active volcanic edifices is key to prevent catastrophic events. The persistent seismicity recorded below the eastern flank of Piton de la Fournaise shield volcano (Réunion Island), both in between and during eruptive events, may give indications on the mechanical stability of this edifice. Whether this asymmetric "cup" shaped seismicity is linked to magma injections and whether it sparks a gravitational flank slide motivates this study. Here we model the elasto-plastic behavior of this volcanic edifice at crustal scale, with the 3D finite-element code Adeli. First, we test the influence of tensile failure, recently implemented in combination to a Drucker-Prager shear failure criterion; a pressurized cavity below a flat top surface triggers shear failure in general, with tensile failure restricted to the surface and cavity tip. Then we include the topography of Piton de la Fournaise in the gravity field. Considering first only elasticity, deviatoric stresses attain about 35 MPa below the volcanic edifice and displacements are maximum in the horizontal east-west direction, reaching 30 m near sea-level. Introducing plastic behavior produces a rather symmetric cup shape plastic domain around the volcano's summit, that extends at depth with reducing bedrock {\it effective} friction (which acts is a proxy for reduced standard friction due to pore fluid pressurization). An asymmetric listric shear zone develops down to -3 km (bsl) only if the tensile strength, cohesion and friction angle are set as low as 1.5 MPa, 3 MPa and 3°, respectively; these values hence provide a lower bound for the edifice's effective strength. The second part of this study explores the influence of an internal overpressure, which is either applied as a vertical inflation source located about 500 m below the surface of the eastern flank, simulating a distal dike, or from a deeper ellipsoid simulating the magma reservoir located at depth ca. 0 km (near sea level) below the summit. The resulting strain pattern forms a cup-shaped shear zone dipping down below the eastern flanks of the edifice, reaching depth -2 km ({\it bsl}) if effective friction angle is $ \leq 5^\circ$. Whereas the deep base of the dike and the eastern edge of the magma reservoir coincide geometrically in the models, the inflating dike produces a shear zone 1 km shallower than does the inflating magma reservoir, the latter coinciding better with the shape of the observed seismic cup. Hence, we propose that this structure is a mechanical consequence of continuous magma supply in the reservoir, coherent with previous interpretations. This means that at least originally it did not need to form as a pre-existing weak zone or a magma-filled structure. However, this shear zone delimits an underlying domain in dilatation relative to a constricted hanging-wall; it may thus promote magma sills. It also branches to the surface with planar radial shear zones comparable to some observed eruptive fissures. The 3D kinematics of this shear zone does not rule out the possibility of a giant flank slide, although it does not appear today as imminent.