The Tibetan Plateau has the thickest continental crust on Earth, and fabrics within the crust that are anisotropic to seismic waves may provide clues to how it reached such extreme proportions and how it is currently deforming. Waveform modeling using a global minimization inversion technique applied to receiver functions computed from 11 stations spanning the north-south length of the eastern plateau has yielded a suite of crustal models that include anisotropy. These models suggest that the Tibetan crust contains 4--14% anisotropy at different depths that is likely a result of both fossil fabrics and more recent deformation. All models contain anisotropy in the surface layer, and for most stations the alignment of the slow symmetry axis suggests a relationship with crustal fabrics associated with E-W trending thrust faults or sutures. Middle to lower crustal anisotropy is present at most stations with a fast axis trending N-S to NW-SE in the south, nearly E-W in the central plateau, and N-S to NE-SW in the northern plateau. This pattern appears consistent with recent ductile deformation due to both topographically induced flow and to boundary forces from subducting lithosphere at the northern and southern margins of the plateau. The orientations of crustal anisotropy determined for most stations in this study are significantly different from shear wave splitting fast polarization directions, implying distinct deformation in the crust and mantle.