A method is intended to produce a covering cover for a seat. This method comprises: - a first step (100) in which two opposite longitudinal edges folded together are at least one elongated piece with two longitudinal edges folded and belonging respectively to two strips of intermediate material in order to constitute two longitudinal sub-parts folded, and - a second step (110-130) in which a strip of foam is housed under each piece, then the two longitudinal sub-portions of each piece are folded under the strip of foam that it houses and under the one of the neighboring strips of intermediate material, then a support layer is placed under each piece with its foam strip which is secured to the folded longitudinal sub-parts.
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