Acceleration by radiation pressure could, in principle, explain the observed relativistic velocity of jets in extragalactic radio sources. The radiative aceleration mechanism is based on radiation beams that are produced and collimated in funnels (vortices) along the rotation axis of a thick accretion disk. These radiation beams accelerate particles to form the relativistic jets. In order to accelerate particles to ..gamma..>1.5, the funnels must be short and very steep. However, such funnels cannot satisfy Rayleigh's stability criterion. Therefore, the radiative acceleration mechanism cannot accelerate particles to high relativistic velocities.