A device for manufacturing a composite material part that includes a resin matrix reinforced by fibers and having a recessed shape with a small opening, whereby the device includes a mold whose shapes are adapted to those of the part to be produced, a compacting membrane and at least one shim that is placed in the recessed zone between the part and the compacting membrane whose function is to transmit the pressure exerted by the compacting membrane to the surfaces of the part that is in contact with the shim. The shim can be expanded and is able to occupy a first state before polymerization in which it occupies a low volume so as to allow its insertion into the recessed zone, and a second state, in particular during polymerization, in which it occupies a larger volume so as to exert pressure on the surfaces of the recessed zone.