The polarization of rodlike polyelectrolytes has been analyzed by Brownian dynamics simulations, using a cube with a polymer in the center surrounded by counterions and byions, Electrostatic interactions both in the cube and beyond the cube were evaluated assuming periodic boundary conditions using Ewald summation. The effect of hydrodynamic interactions on the dynamics of the ions has been evaluated by modified Oseen interaction tensors. For polyions without added salt, the dipole induced in the presence of hydrodynamic interactions is smaller than in their absence for most of our simulated data, but under some conditions the effect of hydrodynamic interactions is rather small. For polyions with 40 and 60 residues, the dipole moment induced perpendicular to the rod axis, mu(perpendicular to), is rather close to that induced parallel to the rod axis, mu(parallel to).