Abstract: The machine comprises a solid matrix (1), a deformable body (2) joined to the surface of said matrix (1), a shaping mould (3) and a securing system system (5) for the fibre structure (4). The matrix (1) is a solid element having a functional face, the geometry of which depends on the part to be manufactured. The deformable body (2) has an initial geometry that depends on the geometry to be given to the fibre structure (4). The shaping mould (3) has the geometry to be given to the fibre structure (4) during the process of adaptation to the shaping mould (3), and the shaping mould (3) is located such that the deformable body (2) is located between said shaping mould (3) and the matrix (1).