We use finite-element models to evaluate the effect of asthenospheric strain associated with the motion of an oceanic plate over a presumed stationary mantle on shear wave splitting observations. Modeled velocity profiles display a clear strain localization within a horizontal shear zone several tens of kilometers wide developed between an almost rigid mechanical lithosphere and a mildly deformed upper mantle. For young oceanic lithosphere, cooling results in migration of the maximum shear strain rate towards deeper levels and progressive widening of the shear zone. Shear strain accumulates with plate displacement. The deformed layer thickness depends on plate age and velocity. Seismic anisotropy depends on the preferred orientations of olivine developed, and thus on the strain field. For a ray propagating vertically (e.g., SKS) the fast wave will be polarized parallel to the flow direction, i.e., the APM. The delay time will depend on the thickness of the sheared layer and on its intrinsic anisotropy. It will therefore increase away from the ridge at a progressively decreasing rate and depend on the absolute plate velocity. The estimated anisotropies agree with seismic anisotropy measurements in old domains of ocean basins, suggesting that, away from mid-ocean ridges, this simple model may provide a first approximation of the mechanism responsible for the observed seismic anisotropy. ¿ American Geophysical Union 1996