Process for molding a part made out of a composite material

The process includes placing in a mold a pile of plies taken from a web of fibers embedded in a thermosetting or thermoplastic material, the plies being arranged according to preferred directions of the fibers, and subjecting the mold to particular pressure and temperature conditions. The process also includes carrying out successive operations of shaping the pile of plies in the mold, at low pressure, carried out progressively at low speed; removing the material in excess protruding out of edge of the mold; carrying out the tightness of the mold from outside; increasing the pressure up to high pressure; raising the temperature of the mold; and quickly cooling the mold.