A model is presented that simulates anisotropy development in a subducting slab from the upper-lower mantle boundary (661 km) to the core-mantle boundary (2891 km). Two phases are considered: orthorhombic MgSiO 3-perovskite and cubic magnesiowuestite (Mg,Fe)O. Single crystal elastic properties at mantle conditions are obtained from existing density functional theory calculations and quasiharmonic approximation. It is assumed that deformation is accommodated by slip. A polycrystal plasticity model predicts strong texture development for perovskite and weaker texture for magnesiowuestite. When averaging single crystal elastic properties with the orientation distribution this results for both phases in weak P-wave anisotropy and shear wave splitting in the upper part of the lower mantle but pronounced anisotropy near the core-mantle boundary (up to 4% for Vp and 7% for Vs). The anisotropy pattern is complex and asymmetric and local heterogeneity is expected. These predictions are consistent with seismic observations.