  For propagating and evanescent vector Bessel beams, we study the
singularities of the Poynting vector (Poynting singularities), at which the
energy flux density turns to zero. Poynting singularities include all the phase
singularities and some of polarization ones (L- and C-points). We reveal the
existence conditions and positions of singularities, which are located at
cylindrical surfaces around the beam axis. We mark the special case of the
evanescent Bessel beam in the form of cylindrical standing wave, that is
singular at any spatial point.
