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The effects of an arbitrary beam thickness and a conducting wall in the Raman‐type free‐electron laser are investigated. To simplify the problem, a two‐dimensional model of a solid nonmagnetized relativistic electron beam enclosed with a parallel plate waveguide is considered. With the aid of the fluid theory for electron beams, the coupled mode equation relating the scattered wave (TE mode) and the electron plasma wave (TM mode) under the influence of the pump wave (TE mode) is derived. By using the solution to the coupled mode equation, together with the boundary conditions on the beam surface, the dispersion relation and the spatial growth rate for the coupled scattered and electron plasma waves are found. From detailed numerical analysis for the properties of the scattered wave, several interesting results are obtained. First, in order to get an appreciable magnitude of the growth rate, the beam width and the separation between the conducting walls of a parallel plate waveguide are required to be considerably greater than the wavelength of the scattered wave. Second, the growth rate becomes maximum for particular values of the ratio of the beam thickness to the separation between the conducting walls. Third, the growth rate can be greater for the pump and scattered waves with even symmetry than for those with odd symmetry.