Geodynamic simulations of the development of lattice preferred orientation in the flowing mantle are used to characterize the seismic anisotropy and shear wave splitting (SWS) patterns expected for the interaction of mantle plumes and lithospheric plates. Models predict that in the deeper part of the plume layer ponding beneath the plate, olivine a axes tend to align perpendicular to the radially directed plume flow, forming a circular pattern reflecting circumferential stretching. In the shallower part of the plume layer, plate shear is more important and the a axes tend toward the direction of plate motion. Predicted SWS over intraplate plumes reflects the asymmetric influence of plate shear with fast S wave polarization directions forming a pattern of nested U shapes that open in the direction opposing both plate motion and the parabolic shape often used to describe the flow lines of the plume. Predictions explain SWS observations around the Eifel hot spot with an eastward, not westward, moving Eurasian plate, consistent with global studies that require relatively slow net (westward) rotation of all of the plates. SWS at the Hawaiian hot spot can be explained by the effects of plume-plate interaction, combined with fossil anisotropy in the Pacific lithosphere. In ridge-centered plume models, the fast polarization directions angle diagonally toward the ridge axis when the plume is simulated as having low viscosity beneath the thermal lithosphere. Such a model better explains SWS observations in northeast Iceland than a model that incorporates a high-viscosity layer due to dehydration of the shallow-most upper mantle