Both the polarization direction of the fast shear waves and the types of deformation within overriding plates vary between the back arc basins of western Pacific subduction zones. The goal of this study is to test the possibility that motions of the overriding plates may control the patterns of seismic anisotropy and therefore the observed shear wave splitting. We calculated three-dimensional models of viscous asthenospheric flow driven by the motions of the subducting slab and overriding plates. Shear wave splitting was calculated for polymineralic anisotropy within the back arc mantle wedge assuming that the anisotropy was created by flow-induced strain. Predicted splitting may differ substantially depending on whether anisotropy is computed directly using polycrystalline plasticity models or is based on the orientation of finite strain. A parameter study shows that both finite strain and textural anisotropy developed within three- dimensional, plate-coupled asthenospheric flow models are very heterogeneous when back arc shearing occurs within the overriding plate. Therefore predicted shear wave splitting varies strongly as a function of plate motion boundary conditions and with ray path through the back arc asthenosphere. Flow models incorporating plate motion boundary conditions for the Tonga, southern Kuril, and eastern Aleutian subduction zones produce splitting parameters consistent with observations from each region. Trench-parallel flow generated by small variations in the dip of the subducting plate may be important in explaining observed fast directions of anisotropy sampled within the innermost corner of the mantle wedge. ¿ 2000 American Geophysical Union