In tokamak H-mode, a large poloidal flow exists in an edge transport barrier, and the electrostatic potential and density profiles can be steep both in the radial and poloidal direction. Two-dimensional structures of the potential, density and flow velocity near the edge of a tokamak plasma are investigated. The model includes the nonlinearity in bulk-ion viscosity and turbulence-driven shear viscosity. For the case with a strong radial electric field (H-mode), a two-dimensional structure in a transport barrier is obtained, giving a poloidal shock with a solitary radial electric field profile. The poloidal electric field induces convective transport in the radial direction, and poloidal asymmetry makes the flux-surface-averaged particle flux direct inward with a pinch velocity on the order of 1 [m/s]. A large poloidal flow with radial shear enhances the inward pinch velocity. The abrupt increase of this inward ion and electron flux at the onset of L-to-H-mode transition explains the rapid establishment of the density pedestal at the transition.