The style of inversion of inherited extensional basins in the Western Alps is investigated through thermo-mechanical modelling. Two-dimensional models consist of a half-graben embedded in a relatively strong crust (basement) and filled with weak syn-rift sediments (cover). We investigate the relative influence of the internal friction (µ) of the basin-bounding normal fault, tectonic burial (h) under an overlying nappe and the geothermal gradient. We use a viscoplastic model with symmetrical shortening. The inherited normal fault is implemented as a curved thin body with a variable friction coefficient (µ) ranging from 0.1 to 0.6. The style of basin inversion is controlled at shallow depth by the internal friction coefficient, whose influence decreases with the increase of both burial depth and geothermal gradient. With increasing burial and/or geothermal gradient, fault reactivation is inhibited and distributed deformation in the basement induces the vertical extrusion of the cover. The basin inversion is accompanied by distributed deformation in the cover and by the shearing of the basin and basement interface. The results are consistent with the style of inversion of inherited half-grabens in the external Western Alps, where no significant fault reactivation occurred owing to tectonic burial underneath the Alpine internal units during the early Alpine collision.