Reactivation of structures inherited from previous collisional or rifting events, especially lithospheric-scale faults, is a major feature of plate tectonics. Its expression ranges from continental break-up along ancient collisional belts to linear arrays of intraplate magmatism and seismicity. Here we use multiscale numerical models to show that this reactivation can result from an anisotropic mechanical behaviour of the lithospheric mantle due to an inherited preferred orientation of olivine crystals. We explicitly consider an evolving anisotropic viscosity controlled by the orientation of olivine crystals in the mantle. We find that strain is localized in domains where shear stresses on the inherited mantle fabric are high, and that this leads to shearing parallel to the inherited fabric. During rifting, structural reactivation induced by anisotropy results in oblique extension, followed by either normal extension or failure. Our results suggest that anisotropic viscosity in the lithospheric mantle controls the location and orientation of intraplate deformation zones that may evolve into new plate boundaries, and causes long-lived lithospheric-scale wrench faults, contributing to the toroidal component of plate motions on Earth. © 2009 Macmillan Publishers Limited. All rights reserved.