Abstract: This invention relates to methods and apparatus for forming composite material components that have relatively complex surfaces. Currently such components are very expensive to manufacture because forming them requires a good deal of time and hand working of the material. In the system of the invention, a flexible membrane (38) is heated to a forming temperature. Composite material (70) is laid on membrane (38) and heated evenly by contact with membrane (38). Fluid pressure is applied to membrane (38) to force membrane (38) and material (70) upwardly against a mold surface. While it is urged against the mold surface, material (70) flow forms to the shape of the mold surface. Preferably, the mold surface and membrane (38) are rotated about a horizontal axis approximately 180.degree. to position the mold surface below membrane (38) before the fluid pressure is removed to allow membrane (38) to move out of contact with material (70).