On the basis of polycrystalline theory describing the plasticity in olivine and enstatite, the flow in a convection cell has been simulated using a finite element formulation. The spatial variations in anisotropic properties are computed from the textures that evolve with the flow. A kinematically constrained equilibrium-based assumption is used to partition the macroscopic deformation among crystals within an aggregate. We model the convection for one specific cell geometry and two sets of boundary conditions. A complete map of textures throughout the cell is obtained. The textured convection cell is structurally very heterogeneous and textures along streamlines do not correlate with the finite strain. The results of the simulations indicate that during upwelling a strong texture develops rapidly. It convects during spreading and is attenuated during subduction. Results are compared with features of the upper mantle. In our predictions the pattern of preferred orientation during spreading is inclined to the flow coordinates due to deformation by simple shear. This is contrary to Hess' <1964> intuition that (001) slip planes of olivine orient themselves parallel to the flow planes, yet the pattern is consistent with natural fabric data. Significant differences are observed as a function of depth within the cell. The variations in the p wave velocities in this textured model mantle are analyzed and correspond well with observed seismic data. ¿ American Geophysical Union 1993