We use forward models based on recent high-pressure experimental data on mantle minerals to predict the seismic anisotropy produced by plastic strain of orthorhombic wadsleyite, the dominant mineral in the upper transition zone. These models predict a weak seismic anisotropy for a polycrystal of pyrolitic composition (60% wadsleyite, 40% garnet) at transition zone conditions: ~2% for P and ~1% for S waves for a shear strain of 1. Both P and S wave anisotropy patterns show an orthorhombic symmetry. P waves propagate faster at low angle to the shear direction and slower at high angle to the shear plane. S wave anisotropy is characterized by faster propagation of waves polarized at low angle to the shear direction. Horizontal shearing results therefore in higher velocities for horizontally propagating P waves (PH) and horizontally polarized S waves (SH), as well as in weak azimuthal variation of SV and SH velocities. On the other hand, vertical flow leads to higher velocities for vertically propagating P waves (PV) and vertically polarized S waves (SV) and to a weak azimuthal variation of SV velocity but to a roughly constant SH velocity. Analysis of global observations of seismic anisotropy in the transition zone in the light of these models supports dominant horizontal flow in the uppermost transition zone, in agreement with predictions of geodynamical models that explicitly introduce phase transitions.