  In this paper we are studying the scattering of massless Dirac fermions by
Schwarzschild and Reissner-Nordstr\"om black holes. This is done by applying
the partial wave analysis to the scattering modes obtained after solving the
massless Dirac equation in the asymptotic regions of the two black hole
geometries. We succeed to obtain analytic phase shifts with the help of which
the scattering cross section is computed. The glory and spiral scattering
phenomena are showed to be present like in the case of massive fermion
scattering by black holes.
