Past studies suggest that phonon confinement and the associated group velocity reduction are the causes of the observed drop in the cross - plane thermal conductivity of semiconductor superlattices. In this work, we investigate the contribution of phonon confinement to the in - plane thermal conductivity of superlattices and the anisotropic effects of phonon confinement on the thermal conductivity in different directions, using a lattice dynamics model. The dispersion relation in a free standing quantum well is calculated and compared with superlattices. We find that the reduced phonon group velocity due to phonon confinement may account for the dramatic reduction in the cross-plane thermal conductivity in superlattice, but the in-plane thermal conductivity drop, caused by the reduced group velocity, is small and can't explain the reported experimental results. This suggests that the reduced relaxation time due to diffuse interface phonon scattering, dislocation scattering, etc, should make major contribution to the in-plane thermal conductivity reduction in superlattices.