The present invention relates to an assembly of a mould (14) and of a cross member (12) of a motor vehicle, the cross member comprising a part (20) that is to be overmoulded which is intended to be placed in the mould, a part intended to be situated on the outside of the mould, and at least one region (22, 24) for housing a mould wall portion (26, 28) interposed between these two parts. The mould wall portion and the region for accommodating it are of essentially complementing shapes and the cross member has, in the accommodating region, at least one change in level (34, 36) by comparison with a reference surface that follows the overall outline of the cross member. The invention also relates to a motor vehicle technical front end forming an overmoulded component produced using the above-defined assembly.