The invention relates to a method for producing a screen (1) for covering a motor vehicle engine, said method comprising the following steps: providing a smoothing layer (2) based on polyurethane foam with a density of between 8 and 15 g / l; disposing said smoothing layer in a thermocompression mold, said layer being disposed between a coating layer (5) and a fibrous layer (6) intended to form a shell (7); perform hot compression of the assembly so as to compress said fibrous layer and compress said smoothing layer so that its thickness becomes less than 1 mm over at least 90% of its surface, so that said coating layer does not is not marked by the surface irregularities of said corresponding face. Figure 1
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