The electromagnetic field of a bunch moving in the presence of a plane grid composed of thin parallel wires is considered by using the averaged boundary conditions method. Two different cases of motion are examined. In the first one, the bunch moves at a constant distance from the grid orthogonally to the wires. The excited surface wave is presented in the form of a spectral integral for a thin bunch with an arbitrary ongitudinal profile. The wave propagates along the wires and does not decay with distance (if dissipation is negligible). Energy losses of the bunch over a unit path are obtained. In the second case, the bunch orthogonally crosses the wire grid. The volume and surface waves are separately analyzed. Properties of the spectral angular density of energy of volume radiation in the far-field zone are described. The energy losses due to the volume and surface radiation are determined. It is demonstrated that the structure of the surface waves in both cases allows determination of the length of the bun