The three dimensional phenomena in the weakly ionized plasma near an anode and a cathode of a Faraday type MHD generator are studied by time dependent three dimensional numerical analyses, where the radiation is taken into account. The Navier-Stokes equations are solved with an implicit total variation diminishing scheme with the radiative heat transfer solved by a finite volume method, while the Maxwell equations are solved by using the Galerkin finite element method. The following results are obtained. In the case of the short circuit load (I = 160 A), the strong Hall effect induces a strong electrical current concentration at the upstream edge of the anode and the downstream edge of the cathode, resulting in high temperature and high conductivity there. The Lorentz force acting at the spot of electrical current concentration may induce inter-anode breakdown, although the present generator does not suffer from inter-anode breakdown. The Lorentz force working at the electrical current concentration at the cathode, on the other hand, brings the concentration current downstream, resulting in strong inter-cathode breakdown. The radiative heat transfer becomes very high locally, resulting in 700 MW/m(3), but the effect can be neglected on the overall generator performance because the plasma is very dense.