The formation of a poloidal shock structure is predicted in H-mode transport barriers, which must be taken into account for transport analyses to clarify the rapid formation mechanism of the H-mode pedestal. The analyses are carried out with edge plasmas in tokamak H-modes, which are induced either spontaneously or by electrode biasing. Two-dimensional structures of the potential, density and flow velocity are calculated with the momentum conservation equation. The validity of one-dimensional L/H transition theory and the iterative process to obtain the two-dimensional structure are confirmed by our analysis. A steep electric field structure both in the radial and poloidal directions induces radial ion fluxes, which increase in the H-mode transport barrier. If the Boltzmann relation is violated, radial electron fluxes are induced. A transport model is constructed, including generation of particle fluxes associated with the two-dimensional structure and reduction of anomalous transport by the steep gradient of the radial electric field. A self-consistent evolution of the density profile is calculated in the L/H transition, which clarifies that the generation of particle fluxes accelerates the density pedestal formation.